You have learned through both the study of magic and of advanced weaponry, how to use your gun not as merely an arcane focus, but as a siphon for your magic.

DISCLAIMER 1:  This is probably not super balanced. It is still a work in progress and is currently being playtested.

DISCLAIMER 2: This is based on a mixture of WoTC's Evoker Wizard, and Matthew Mercer's Gunslinger Fighter.

Powder and Blade

You gain proficiency with a firearm or ranged weapon of my choice, my signature weapon. While wielding this weapon and nothing else, I may use INT for to hit and damage rolls. My signature weapon counts as magical for the purpose of overcoming resistances. I may use my signature weapon as a spellcasting focus.

Evocation Savant

Beginning when you select this school at 2nd level, the gold and time you must spend to copy an evocation spell into your spellbook is halved.

Spell Sniper

Beginning at 2nd level, you have learned how to guide your projectiles, hitting enemies and avoiding your friends. If you cast an evocation spell with an area of effect, you can instead choose to hit 2 + the spell's level creatures. They must be within half of the spell's radius distance from each other. The chosen automatically fail on their saving throws vs. the spell.

Firearm Proficiency

Starting at 3rd level, you have gained a strong understanding of how projectiles work. You gain proficiency with firearms and ranged weapons.

Grit

You gain grit points which I can spend to perform various "shot" attacks with my firearms. Grit points must be spent before the roll; only a single grit shot can be used per attack. I regain 1 spent grit point when I use a firearm to score a critical hit or killing blow with a regular bullet. Grit points cannot be used in conjunction with enhanced bullets

Deadeye Shot

[1 Grit point] You gain advantage on the next attack roll you make with a firearm this round

Piercing Shot

[1 grit point] When you hit with a ranged weapon that deals piercing damage,  you can also hit the targets behind it. You make an attack roll for everyone in a line directly behind the target. This continues out to a range equal to the weapon's first range increment. Only the initial attack roll can misfire.

Trick Shot

[1 grit point; DC 8 + Dex mod + Prof Bonus] You can aim for a specific body part, granted you can see that part of the target's anatomy:

Head: Constitution save or it has disadvantage on its attack rolls until the end of its next turn

Arms: Strength save or it drops one held item of my choice.

Torso: It is pushed up to 10 feet directly away from me.

Legs/Wings: Strength save or it gets knocked prone.

Violent Shot

[1 or more grit points] For each grit point you spend, the attack gains +2 to the firearm's misfire score. If the attack hits, you can roll one additional weapon damage die per grit point spent.

Gunsmith

At level 3, you have studied complex diagrams and fixed your gun enough to be able to replicate the construction. You gain proficiency with tinker's tools. You can use your tinker's tool to craft ammunition and repair damaged firearms. You can even use them to draw up and create new ones (DM's discretion).  Some intricate and experimental firearms can only be accessed through crafting. 

Enhance Bullet

At level 4, you have learned how to infuse your projectiles with magic. You can spend an action and use a spell slot to imbue up to 4 pieces of ammunition with a spell that will be triggered on impact. The spell lasts 1d10 + 1d4/sl hours. You can instead choose to imbue the whole chamber with a spell. If you do so, you need to fully empty the chamber before you can change the effecting spell. If I reload before the chamber is empty, the spell cannot be changed. This spell lasts for 1d4 hours outside of combat. If I use an imbued chamber with an enhanced bullet, the higher level spell is cast. If the higher level is the bullet, the chamber loses the retained spell. If they are equal, both spells are wasted, and the gun misfires normally.

Magic Misfire

At level 5, your magic can sometimes be too much for your simple weaponry to handle. On a misfire with an enhanced bullet, the imbued spell automatically deals the average damage to the target, but I take a piece the spell's damage and must make a strength saving throw (DC 10 + misfire score) or be knocked prone. The weapon also misfires normally. If the target is required to make a save, then the misfire score becomes inverted. For example, if the misfire score is 2, the gun misfires on a 19 or 20.

Second Action

At level 5, you can make two attacks instead of one on my turn. Using an enhanced bullet now takes 2 attacks instead of one. Regular ammunition is unaffected.

Potent Cantrip

Starting at 6th level, your damaging cantrips affect even creatures that avoid the brunt of the effect. When a creature succeeds on a saving throw against your cantrip, the creature takes half the cantrip’s damage (if any) but suffers no additional effect from the cantrip.

Empowered Evocation

Beginning at 10th level, you can add your Intelligence modifier to one damage roll of any wizard evocation spell you cast.

Lightning Reload

At level 15, your reloading skills have increased dramatically. You can reload any firearm or ranged weapon as a bonus action.

Vicious Intent

At level 18, your ranged attacks score a critical hit on a 19 or 20.