(Note: What I write is largely setting agnostic, but not necessarily system agnostic. It is usually constructed from a DnD/Pathfinder/fantasy viewpoint. You may or may not find it applicable to systems you run)
If you asked a commoner what a familiar was, the answers would range from lax presumptions of its status as a menial laborer to hushed whispers of a magical weapon. Soldiers view them as spiteful, eerie omens best not seen with your own eyes. Were you to ask the clergy, they would rattle off accusations towards the witches about their demonic "masters" (they will conveniently forgo mention of their branch of Witch Hunters who take on familiars to guide their hunts). In truth, none of these are the whole story, but neither are they patently false.
Familiars
Familiars are so named because they are formed around a portion of the mage's mind. Specifically their subconscious. It taps into their thoughts yet voiced, dreams, and subliminal thinking and forms a large percentage of its personality around it. Like a fractured mirror of the mage, they are eerily similar, but still yet distinct. Be they witch, wizard, or other kind of thaumaturge, it is always this portion of the mage's mind and is forever placed within the familiar. This is still accessible through a mental link that forges as a result, but like the abilities that form, it takes time to adjust and deepen the bond.
Obtaining a familiar is, therefore, no small ask of a mage, which begs the question of why they would willingly sequester part of their mind and personality within another being. The simplest answer is that without a familiar most mages would never graduate past mastery of cantrips, rituals, and circle magic.
Familiars are magical fonts first, and teachers and guides second. They are an external analog to the internal magical reservoirs that inheritor mages - those born with innate magical aptitude - possess, and are responsible for tutoring, deliberating with, and protecting a mage through their journey of magical growth. The majority of mages must seek out a familiar in order to advance their magical abilities. For education, but also so that they may cast at all (the amount of magic held within an average person that is not an inheritor mage is insufficient to cast even minor spells to completion).
Familiars are quite complex, and their rarity is sourced most in the steep cost of procuring one. In order to obtain one, a mage must first instigate a ritual of summoning. However, this ritual does not summon a familiar, but in fact summons a being known as an iriyani.
Iriyani
An iriyani is a specter. An undead. They exist on the Ethereal Plane and are souls that have lived so long that they have forgotten why they died, and why they have not been able to move on. There are two kinds of iriyani, those who originate from the Realm of the Fey, and those who originate from the Planes Below. Both were once beings of extremely powerful magical ability. It isn't clear what propels souls from these origins to become iriyani, but it is presumed that it must have something to deal with how these souls innately process, form, and maintain contracts and oaths. They have all but lost every last shred of normal behavior they would otherwise possess, and this has been overwritten by an intense desire to feel. Feel, in this case, as mortals do. Those who call upon the iriyani know that such a hungry desire will cost them heavily.
When a mage prepares to summon an iriyani, the incantation they recite in the ritual is the only differing factor. Scholars and other theurgical types that perform this ritual will call forth a "Fey Iriyani". Witches and other coven members will recite the incantation that beckons a "Fiendish Iriyani".
Upon being summoned, an iriyani, regardless of association will lash out. Thus, it's important that a ring of binding glyph be carefully laid to ensure safety of the mage. The pangs of urgent need are plainly seen on the iriyani's "face" (they can and do take many forms, and mages at least know that they crave humanity's essence). It is at this point that the iriyani will calm, and demand parlay. A mage will humbly request aide in the form of a familiar, and the iriyani will demand a portion of the mage's fundamental behaviors.
What this means depends on the iriyani summoned. The scholar's iriyani will require one of their virtues. The witch's iriyani will demand one of their sins. Aside from this being a way to experience something other than the empty existence they hold, they have convinced themselves that this is a method that will help them pass on.
A wizard will decide which of their virtues to yield: chastity, charity, temperance, diligence, kindness, patience, or humility. For a witch: lust, greed, pride, wrath, sloth, gluttony, or envy. The decision is not trivial. On the surface, removing one of your virtues sounds suspect, and removing a sin would seem to make you a better person, but these are both incomplete thoughts needing more context. Once decided, a Fey Iriyani will bind you at your word of agreement. A Fiendish Iriyani will produce a contract to sign - a holdover from when they were among devilkin.
It is from this point that things get complex.
Crafting the Familiar
The iriyani will take your virtue or your sin in confounding ways. Mostly, this manifests as a stunted ability to display the trait that was yielded for quite a long time. The piece of humanity given then funnels into the iriyani, which is expected. They asked for it specifically, after all. But this does more than the iriyani would ever let on.
At this point, the iriyani will fetch the body of an animal from the surrounding area, never anything too big. Then, they will thieve away your subconscious and force it into the creature. Thoughts are not had unless explicitly voiced in one's own mind, and no dreams are had for the first week of acclimation. Bizarre as it is, this is not immediately known to the mage. At this point, there is little that is remarkable about this creature. A turtle remains a turtle, just with the ability to hear your thoughts.
What makes the magic happen, so to speak, is found when the iriyani retreats briefly to the Ethereal Plane to find a suitable spirit. Iriyani, despite their pitiable existence, learn and learn well the plights of ghosts and spirits that dwell alongside them. They form friendships that are never satisfying to their end, largely culminating in a one-sided relationship subsisting on the desperate loneliness of the specter they come across. These ghastly beings run a range of abilities, but for the purpose the iriyani has in mind, they all function the same - to create an ethereal tether from familiar to mage and to create the magical font for use by the mage. Unbeknownst to the mage (but clearly understood by the iriyani) is that this process also creates a tether from familiar to the iriyani.
The iriyani will return; the familiar in tow with a capable, cooperative spirit held within. The process is essentially a heightened and calculated form of possession by two entities. The spirit elevates the creature to a being worthy of mention and forms an ethereal tether, while the fraction of mind allows it to talk (telepathically or otherwise), think, process, share senses, and teach. The tether works in both directions.
All of this happens quickly. And all of it seems worth it, in the end. A piece of your humanity is a small price for the ability to bend reality to your whims.
But there's always a catch.
Consequences
After the familiar is crafted, you are given a strict command. Always obey your familiar. If you don't, you lose it.
It makes sense - they are supposed to be educators that understand how to foster growth of your magical ability. They are tasked with setting you on your path of knowledge. They are to direct you to greater power.
A lot of mages reason that the familiars are actually cosmically linked to some source of knowledge that the iriyani must have the ability to tap into. Well, it isn't too far off. In reality, the iriyani is the source that is being tapped. And what is "tapped" in this case is twofold. Remember, the iriyani were once powerfully magical, and though they forgot who they are, they have a magical reflex. They know what to do, even though they don't know why. So "tapping" the iriyani means access to an innate awareness of how to become a better mage. Conversely, the goals and methods they have for teaching are largely predetermined - based upon which piece of humanity you forsook.
The piece of humanity yielded acts as a seed, growing in time with the mage's progress. The iriyani grows in power day by day, and they leech off more emotion from this essence as if it were some strange tea, steeped in the water of their soul; stronger with each second.
But as far as what this looks like?
A scholar yielding their kindness, for instance, will hamstring their own politeness for the foreseeable future, and leave them prone to jealousy in ways unnatural to them. Their familiar, on the other hand, is immune to the emotional handicap, and is taking orders from the iriyani. The iriyani, by the way, which will become an embodiment of kindness.
On the flip side, a witch yielding her pride will lose confidence, gain self-doubt, and will be less evil than they once were, technically, but will be following the lead of a being fueled by pure arrogance.
In either case, the mage is afflicted by being less of what they gave up, only to study under the tutelage of an entity that will shape them and guide them in the shadow of this ideal. But even were a mage to learn about all of this, it would seem at first glance like wizards and the like have it easy. Give up kindness and learn to be kinder by the day.
Again, there's always a catch.
Let's not forget that the iriyani is a being desperate to pass on, and until then, they are desperate to feel. The piece of humanity they are given is like feeding an addiction, and addicts never have enough. What is billed as kindness is, in fact, just a pleasant mask to sell all of the ideas, goals, and aspirations you are given.
You will be coaxed to kill the wicked king. After all, his atrocities have brought many to an early grave. It's hard work, but sometimes the kindest act you can perform is one on behalf of others, no matter the cost, your familiar will tell you. Murder will be rationalized. Stealing, theft, worse. And why? Because as if some cruel spectator, the iriyani is hoping to gain entertainment from your "deeds". And with every milestone you reach, the stronger a feeling their empty souls feel. Mages catch on by this point and realize that their familiar has an agenda.
But by now it's too late. The mage has gotten a taste for power, and should they decline, the iriyani will end the agreement, and the mage will be without familiar and piece of humanity alike. Thus begins the real journey of a mage: how to keep the familiar while also not falling prey to temptations that would surely end poorly for them.
Witches tend to have it a bit easier in this case, as many willingly sign up for this. But there are those that realize the pact is more than they ever bargained for, and they, too, experience the same tightrope walk.
In either case, succumbing to the allure of power is the desired end, and many a mage fails to resist.
Losing a Familiar
If your familiar dies, you lose your magical abilities. But the iriyani will happily make another. It will cost another piece of your humanity, though. This is dangerous, because now there are twice as many facets by which they can mask an action as palatably as possible. You are not otherwise negatively affected by losing your familiar, though. Nothing happens to the portion of your subconscious - the ethereal tether ensures that it is shunted back to you in this exact event.
Other Abilities
Being able to cast and learn magic is fine and all, but there are a number of abilities that can develop as the bond deepens.
At the beginning, a familiar can detect surface thoughts as well as subconscious thoughts (the mage ceases having them within their own mind, and instead they are first heard by their familiar). This works in reverse as well, but requires some focus. After about half a year together, the mage has learned how to think in their own mind, away from detection by the familiar, but can still be analyzed if the familiar actively attempts to.
Soon after, slight focus can allow the familiar and the mage to sense what they other feels within about thirty feet of each other. The other is aware of this occurring, but cannot stop it. With dedication, the mage can learn to enter a trance and can extend this range indefinitely, but this predictably leaves them vulnerable. In this trance-state, the familiar is effectively hosting the whole consciousness of the mage, and the mage could then speak through their familiar to allies.
Familiars host their mage's dreams, but is never asleep or unconscious while they are occurring. They are able to analyze and manipulate them, and can even talk to the mage in them.
Familiars are quite hardy, and can only be fundamentally hurt by things that can harm ghosts - so magic, ghost touch weaponry, and anything of that sort.
Interestingly, there comes a point where a familiar's mind (your subconscious) has been subjected to the tug of war between your preferences and the iriyani's commands for so long that they begin occasionally acting on their own. Partially, this is shaped by the spirit that is within them. This is called a personality split, and when this happens, the familiar is given free range to act on their own behalf. It's nigh undetectable at first. But soon the mage will notice that the caliber of requests has been easy to manage. The familiar will sense the awareness and confirm it.
But that doesn't mean the familiar is on the mage's side from then on out. The spirit within them still has a say, and is largely able to wedge itself in the decision making process when this split occurs. In some cases, the familiar's desires are even worse. But this is where it becomes difficult to navigate - any request could, theoretically be from the iriyani, and must necessarily be done.
From this point on, little changes. The cycle continues. The two will dance in lockstep until the mage perishes, and though burgeoning casters are warned of the steep prices in veiled metaphors (it would be anathema to the iriyani to state it upfront), mages by the dozen fall prey all the time. Most lament it, but some - the truly noteworthy - harness it, and turn it into their greatest tool.
The work of a mage is not easy, nor is it ever complete.
Afterword and How to Use This
Hey, it's a late post for a few reasons. Last week we got hit hard by a winter storm. This is code for I got distracted by having some snow to play in, but also my partner was off, so we spent time together on her days off.
I initially had a different idea that was a bit more straightforward, but it was too generic and low-effort. This feels right enough to hit the sweet spot of "a bit creepy, but also pretty reasonable", but I'll admit it's a tad bit convoluted at parts. I think mostly it was because this was really difficult to get out of my head for whatever reason (I didn't even say all I had to say). But I do like it a lot, overall. It turns the iriyani into a type of "patron", which works exceedingly well for the witch, and is not negatively impacting for the wizard. I think it also has a lot of fleshing out that allows familiars to play a peculiar role at the table.
Let's say you wanna use it.
In my mind, I mostly see it going like so: Let's say the wizard is starting with a familiar. They'll need to know all of the parts of the ritual, but they should absolutely not know that the iriyani is malicious/self-centered. They should be encouraged to discuss with their familiar, and the GM should issue commands that are purely in the spirit of guiding the wizard's progress. Occasionally, they should slip in "ideas" that are really just fodder for chaos. They should probably realize the iriyani is the one calling the shots no earlier than level 5, if it can be helped.
Witches aiming for a good party are, in my opinion, the most ripe for a compelling inclusion of this. They're likely to have malicious tendencies from the coven they hail from (or from whatever misguided path they took to get there sans coven), but have likely come to realize quite soon that their malefactor is not all it's cracked up to be. Seems compelling to see them try to find ways to turn orders from the next best thing to a devil into something good, lest they lose their magic.
The iriyani (through the familiar) should always operate with a distinct vagueness. Vagueness not in request or suggestion, but vagueness in outcome. They should sell the requests, demands, and other actions as reasonable for as long as possible. There needs to be a genuinely good argument for what they suggest. And so, until the jig is up, they'll never request brazen tasks that clearly show their hand. They want to corrupt the mage as part of their essence, and the less upfront they can be about it, the more payoff there will be when the mage finally pieces together that their familiar has been against them all along.
But perhaps the best part of this in my mind is what it does for the NPCs. Familiars in my experience are under utilized and mostly just set pieces to say "THIS IS A MAGICAL PERSON". I think it's interesting to know that everyone who is a mage gave up an ultimate piece of themselves, and now is often acting in deceitful ways. If not to ensure the iriyani's goals are met, then to ensure that they aren't.
I will also say this is probably best used for settings where magic is not too, too common. It can work with commonplace magic, but it gets a little awkward when thousands of mages all have this scenario. An alternative might be to keep everything the same by the book, and to have a few of the NPCs or players have this as an option for calling a familiar. Perhaps enticing as an option by it not costing any gold?
I probably missed some parts, but it's late for me, and this is already dragging on.
I hope you enjoyed reading. If you end up using this, just consider sending people my way!