
avr |

A grenadier alchemist with the explosive missile discovery and a pistol might qualify. You could do this with or without a level in gunslinger.
A battle host occultist could use the gun as their bonded item, making it immune to the broken condition. This would allow it to give extra damage to spells as the evocation implement, and they could use legacy weapon from the transmutation to enchant the gun when necessary. You'd need a level in gunslinger or similar first in order to get proficiency as you'd really want proficiency with your bonded item at first level.
Spellslinger can be coupled with other classes (you only need 11-12 Int for the one level of wizard) and there are arguments for going with a full caster. Some variety of sorcerer for impressive blasting, or any variety of divine caster (cleric, druid, oracle) for 3/4 BAB and buffs as well as blasting. Admittedly the druid would do more battlefield control than blasting.

BadBird |

The issue with builds that combine firearms and magic is that you generally need 5 levels of a 'gun' class to really be good with a gun, while you can't really give-up 5 levels of spellcasting and be a good spellcaster. The 5 levels of 'gun' class is due to the fact that that's when gun-classes let you add your DEX to gun damage rolls.
There are a few niche options like Eldritch Archer Magus that can bridge the gap, but it's not really a full-on "evoker" Wizard type.
The Spellslinger Wizard kind of works, but it has it's limitations.
A Strength Patron Witch/ Gunslinger/ Eldritch Knight type character might be able to pull-off reasonable damage through buffing spells.
The Trench Fighter Archetype grants DEX on gun damage at level 3, so you could maybe build a Trench Fighter/Wizard. The thing is, Trench Fighter is from an adventure path that's set partly in World War 1, so it's kind of obscure... some GM's may scoff at using it.

Dragonchess Player |

Well, you could go tiefling (Prehensile Tail alternate racial trait) gunslinger 1/wizard (spellslinger) 1/arcanist (blade adept) 6/eldritch knight. You don't get Dex to damage on the gun, but any round you can choose to shoot spells through your gun (with bonuses from the gun and a x3 critical multiplier) or use the Spellstrike exploit to channel a spell into a sword (probably a rapier to use Fencing Grace; the prehensile tail can hold the gun to meet the "free hand" requirement of casting or Fencing Grace, just as it can hold the gun for reloading without dropping the sword). The Eldritch Blade exploit (take using the Extra Arcanist Exploit feat at arcanist 5 or eldritch knight 1) advances your black blade based on caster level rather than arcanist class level (making the Magical Knack (Arcanist) trait even more useful).
You don't get to full attack and cast with Spell Combat like a magus, but you get more and better spells, can change your prepared spells to suit the opposition and still cast spontaneously from your spell slots, and can take the Arcane Weapon and School Understanding (Evocation/Admixture) exploits (using the Extra Arcanist Exploit feat) to add weapon bonuses/abilities and change spell energy types on the fly.

Avoron |
I'm going to toss in a suggestion for Spellslinger Wizard 3/Vivisectionist Alchemist 1/Arcane Trickster X, with Accomplished Sneak Attacker to meet the prerequisite and Magical Knack to keep your caster level up. You now have full sneak attack progression, almost full casting progression, spellslinger and arcane trickster goodies, mutagen or cognatogen, and a smattering of extracts. You can rely on high-Dex touch attacks to hit and sneak attack for damage, alternating spells and bullets as the situation requires. Definitely not optimized, but it's doable.

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Do the suggestions have to be PFS legal?
If not then I suggest looking at the Arcane Gun Wizard Archetype. Dipping Sorcerer for Draconic/Orc might be something you want to consider.
Another idea would be to go Eldritch Archer Magus and either use a bow or dip into Gunslinger.
For PFS legal ideas then an Arrowsong Minstrel gets Ranged Spellstrike at level 6. Though this one does require a dip into Gunslinger to be able to use it properly with guns. And once more a dip into Sorcerer might also be something you ought to consider.

Dragonchess Player |

I'm going to toss in a suggestion for Spellslinger Wizard 3/Vivisectionist Alchemist 1/Arcane Trickster X, with Accomplished Sneak Attacker to meet the prerequisite and Magical Knack to keep your caster level up. You now have full sneak attack progression, almost full casting progression, spellslinger and arcane trickster goodies, mutagen or cognatogen, and a smattering of extracts. You can rely on high-Dex touch attacks to hit and sneak attack for damage, alternating spells and bullets as the situation requires. Definitely not optimized, but it's doable.
For a Sneak Attack shooter, I'd go wizard (spellslinger) 1/brawler (snakebite striker) 1/arcanist 4/arcane trickster with Accomplished Sneak Attacker feat at 3rd character level.
The 10 min duration on the mutagen (for a level 1 alchemist) that takes 1 hour to make (and you can only have one in existence at any given time) is, IMO, less useful than an extra +1 BAB; effectively, the mutagen gives a +1 over the brawler route in one or maybe two fights. Your route will also have +1d6 on the Sneak Attack from 6th to 16th character level.
Also, the spellslinger having to give up cantrips and take four opposition schools makes using it as a dip (since all of the class features are gained at 1st level) for arcanist a "better" choice: you regain cantrips (unlimited acid splash and/or ray of frost from your Arcane Gun... with the gun's bonuses and at x3 critical multiplier, plus Sneak Attack when applicable), you no longer have opposition schools as an arcanist, and you gain the spell slot flexibility of the sorcerer while retaining the day-to-day flexibility of preparing different spell selection like a wizard. You give up two levels of casting progression instead of one, and the arcanist is already a level behind in gaining higher level spells, but the benefits (the mentioned School Understanding exploit with Evocation/Admixture is a big benefit in itself) are pretty darn good.
Alternately, magus (eldritch archer) 2/brawler (snakebite striker) 1/wizard (spellslinger) 1/magus +2/arcane trickster (advance magus spellcasting) also works, gaining light armor use and a higher BAB but losing higher level spells (magus progression).

Avoron |
The problem with those progressions that greater invisibility is your best source of sneak attack damage, and those arcanist and magus builds wouldn't get it until 10th or 12th level. I'd almost prefer forgetting spellslinger entirely and just going with three levels of admixture wizard.
Or wait, here's an idea. What about a samsaran elements patron witch, taking something like witch 3/brawler (snakebite striker) 1/wizard (spellslinger) 1/arcane trickster? You're only down one level of sneak attack and two of casting, and you can snag greater invisibility off the summoner spell list as early as 7th level, along with a few of your favorite arcane blasts.

relativemass |

(Elf or Human) Wizard and gets feats like Spell Focus and Spell Penetration (after ~10th level many creatures have spell resistance). Eventually you will want to get Spell Perfection. Avoid Elemental Specialization since you will eventually fight outsiders and other creature with arbitrary energy resistances/immunities. Try to get one or two a Rods of Elemental Spell or several force spells to deal with creatures with energy resistance/immunity. Metamagic rods can help you a lot.

Dragonchess Player |

The problem with those progressions that greater invisibility is your best source of sneak attack damage
Vanish. Blindness/deafness. Obscuring mist and a goz mask.
All available much earlier than greater invisibility, even for a single-classed wizard.