Weapon and Medical question Eye Gun

You'd be in for one hell of a headache. Even something as small as a .22 cal. has a kick to it, with over 100 foot pounds of energy.
Another problem, you need a barrel to guide the projectile. There would be barely enough room for the round inside an adult eyeball.
You'd be better off building a laser.

What about a weapon trained using eye movement? Where he looks the weapon points, that sort of thing. Could you use that? Any gun would have enough kick to not only destroy the eye, but probably kick it back out of socket doing damage. I'm guessing you replace a real eye with a fake eye. If you must use a bullet and have it inside a fake eye, you could design a kickless system, I mean it's your world and it's not like there are any guns like this.

Second thing you'd have to worry about is heat. Guns get hot when you fire them, you're dealing with chemical reactions, you're risking powder burns all over your character's face as well when the gun is fired as there is no external barrel, the gun powder that's on fire when the bullet comes out is going to hit your character's skin.

So presumably the eye is non functional. For how long has it been non functional? After a while a blind eye starts to become unlinked to the other eye and starts to wander. It's the rolling eyes that freaks a lot of people out to the point that many blind will wear sunglasses.

How about a non-ignition launcher, spring-loaded or something like that, and the projectile is rocket-powered, with snap-out fins, and it's designed to explode slightly after impact, sure to penetrate the target and go kablooie! inside. Oh, and the iris is like a little Gatling gun, capable of firing a dozen or so of these little buggers.

Of course I like the laser beam idea, too.

I think it could be done, well enough for sci-fi anyway. It would require a lot of high tech stuff. I don't think there would be enough room in the eye socket for a decent firearm. Something underpowered, sure. How vital are the parts of the brain directly behind the eye socket? If they are expendable, then you could have a tube running all the way back to the back of the skull and secured there, at the back of the eye socket, and at the front of the socket/skull with titanium.

Then you could put a recoil spring behind your gun to spread out the impact (make it occur over a longer period of time) and transfer it into the three plates.

The extra room would also give you space for a chamber of about a half inch, a decent sized rifled barrel of about two inches, plus a silencer/recoil compensator for the last inch.

You could have special cartridges made with flashless, quick burning powder to eliminate muzzle flash and reduce powder burn. Plus they could be loaded with just the right amount of power for that sized barrel.

Naturally, this would be a one shot deal. You could probably project a 95 grain 9mm bullet at about 800 feet per second, generating 135 foot pounds of energy. A little more than 1/3 the normal power of such a bullet, but still deadly enough with good shot placement.

Why not make it something spring-loaded, like a poisoned dart? There would probably be enough room for it in an empty eye-socket if you fiddle with the science, but an actual gun just ain't happening. Even if a sci-fi setting I just wouldn't buy it. The concussive power from firing even the smallest of guns from within your head would really mess you up. The energy wouldn't dissipate very well considering the socket would basically serve as a bone echo chamber, you would risk tearing blood vessels in the brain that could cause internal bleeding in the skull, the heat and powder burn would most likely hurt your face pretty badly, and it would probably tear muscle in the neck from the recoil. If you have ever fired an actual gun, you still feel it in your hands pretty good even with a proper stance and a ton of muscles along your entire arms working together to hold it in place. Your head doesn't have that advantage.