There's actually a Wizard archetype called a Spellslinger. You can cast any ranged touch attack, cone, line, or ray spells through the gun. But you can also use regular gun attacks too. It gets Exotic Weapon Proficiency Firearms and the Gunsmithing feat at level one.
Wizard (Spellslinger) 1 / Witch (Havoker) 19 ((Or kineticist if you want))
Enchant a firearm with the Conductive weapon property. Fire spells through the weapon (or just fire the weapon) and if targeting anything within 30ft, use a swift action to channel your kinetic energy blast through as well. I made a quite bad@ss little gnome character that did this in our Skulls and Shackles game. I used Reach Spell (Metamagic) a lot to turn the tastey witch touch spells into ranged spells.
You could also us the Eldritch Archer or Myrmidarch archetype for the Magus to get ranged spellstrike instead, if you want something already prepackaged but that would require a spell, unlike the energy blast method.
Spellslinger is interesting, but I think it gives up way too much for what you get. Cantrips sound like a really weenie thing to give up, but its more powerful than you'd think.
But the part that sticks in my throat is 4 opposition schools. No bonus spells. None of the joy and twice the pain of any other wizard school. Thanks, but I'd rather be any other wizard that pays for a musket and casts my spells the old fashioned way.
That is why you only take one level. Your other spellcasting classes can channel spells through the gun without a problem, and aren’t hampered by the four opposition schools. Take your first Spellslinger level at character level 5, if you wish. Save your wizard 1st level spells for low level utility, like feather fall or shield.
Spellslinger 1 then either of the two ranged Magus archetypes is the best route for this.
Some actual levels of Gunslinger or Gunchemist or Vigilante Gunmaster for some actual deeds, and 1 level of Spellslinger, and the witch stuff would be the most flavor. It's a cursed pistol and shoots curses.
I actually tried to make a Spellslinger myself. I was told I spent too many feats on the gun stuff and not enough on the magic. I just wanted a guy that could shoot ice.
1 level gunslinger or picaroon swashbuckler
Then Eldritch Archer Magus.
The magus archetype doesn't look for a "bow" it looks for a ranged weapon and gives you ranged spellstrike, and the ability to cast with your hands full so long as you're holding your bonded gun.
I played a gnome spellslinger in Dragon's Demand once. Ended up creating a cult that worshipped my pistol. Good times.
It's a terrible archetype, but fun to play. Our game was pretty non-serious though, probably helped.
I made a homebrew Gun Bloodrager archetype: Savage Spellslinger. I kept updating the class during playtesting, first to tone down overpowered abilities and then to get the right flavor in combat, so the ninth version is the one that works.
I gave cantrips to the Savage Spellslinger so that she could use Mending to fix a misfired pistol in ten minutes. This meant the class did not need Gunsmithing. Ordinarily the class would buy their first pistol when the character can afford it and buy her gunpowder from a merchant. My playtest character was given a pistol as a reward at 2nd level.
The Savage Spellslinger is not what most people want out of an arcane caster or a gunslinger. Her rate of fire is one shot per round. Her spellcasting has few spells per day. For dealing damage, mostly she functions as a barbarian. I found the class amusingly versatile.
I absolutely adore the "gun mage" and have been considered writing a guide overviewing all the diverse options to do it. Here's an overview of some of my favorites:
Fighter (Trench Fighter) 3 / Wizard (Spellslinger) 5 / Eldritch Knight
These archetypes are a match made in heaven, and complement each other perfectly. The bonus feats from Trench Fighter means you can cover all your standard gunslinger feats and still have room for prestigious spellcaster at 9th level when you enter Eldritch Knight, even a non-human. The arcane gun class feature will go unused, since the risk of an overload is not worth it. This build doesn't have the feats to blast effectively anyways, so you may as well just oppose evocation.
In practice this build plays like a 3/4 BAB 6-level caster class. However, at high levels it matures into an utter monster as at 20th it will have +16 BAB and 9th level spells. If Trench Fighter is not available, one level of Siege Gunner Gunslinger or five levels of Musket Master Gunslinger are also possible, but that results in a steep drop in either attack power or casting power respectively.
Gunslinger (Mysterious Stranger) 1 / Sorcerer 6 / Eldritch Knight
The Mysterious Stranger has the ability to apply Cha to damage on firearms. This has a natural synergy with Sorcerers. Thanks to bloodline mutations, this is one of the best ways to mix blasting with firearm attacks, since Sorcerers can get away without feat investment.
There are two catches with the build. First you don't qualify for quick clear, so you need to use the mending and jury rig spells to handle misfires. This becomes less of an issue at high levels when Quickened Jury Rig becomes more economical, but it's annoying at lower levels. The second catch is that you're incredibly reliant on grit to function, and can easily run through one point of grit per round. If you run out of grit, it can be very hard to start accruing points again.
Gunslinger (Mysterious Stranger) 1 / Bard (Juggler) X
This is a cute little build that uses the Juggler's ability to literally juggle his held items to dual wield firearms while still retaining the option of casting spells. This sort of combat style is really hard to pull off in Pathfinder, so a combo that has abilities that pull it all together gracefully is worth mentioning. It's extremely feat intensive, but if this is what you want to do it's the best way to do it. Otherwise most of the same synergy and issues as the sorcerer version apply.
Magus (Eldritch Archer)
There are three ways of doing this build: single-class with feat investment, a one-level gunslinger dip (usually siege gunner archetype), or a one-level spellslinger wizard dip. The Eldritch Archer synergizes extremely well with firearm attacks, since it hates losing its spells to misses. Using a firearm to make those ranged touch attacks solves that problem completely. It's very feat intensive, however, so a one-level dip to cover that problem is recommended.
Wizard (Spellslinger) 1 / Other Caster X
The arcane gun class feature isn't limited to just your wizard spells, so you can freely mix it with the Sorcerer, Arcanist, or something like the Havoker as previously mentioned. This is more of a caster heavy build that doesn't bother with basic firearm attacks, but it's a simple way of getting around the worst restrictions of the Spellslinger.
Spellslinger lets you add weapon enhancement bonus to spell DCs, IIRC.
So anything for Divine casters?
Well ... yes. In fact, combining Spellslinger with a Nature Fang Druid can be fairly potent as well. Having the ability to boost the DC of your spells with the Spellslinger ability AND that of Studied Target will make your spells incredibly hard to resist. Nature Fang even has the ability to pick up Grit and Deeds through the Slayer Talents, as well as Ranger Combat Styles. The thing you have to get past is a Druid using a firearm, hahaha.
Shaman's with the Wave Spirit can combine the Crashing Waves hex with any water spells (or any elemental spells if you add the Benthic Spell metamagic feat), you get the ability to force a fort save vs knocking your opponent prone with every spell. Adding certain "bad touch" spells from the Cleric list to your shaman casting list, and using Reach Spell to deliver them also has very high potential for shenanigans.
Going to say that starting as a Eldritch Archer Magus at first level isn't bad. You start play with a Wizard's Arcane Bond object that is a ranged weapon. Masterworked and common materials. No price limit. You could start play with a cylinder rifle.
So why dip into gunslinger?
Proficiency, gunsmithing, and quick clear.
I just took a look at Eldritch Archer. I might use that for my character.