Here you can find a guide to the available innovations, please refrain from using any Unearthed Arcana.
Below are some options relating to this setting's Pact of the Trigger:
Agonizing Shots
Prerequisite: Pact of the Trigger feature
When you cast a cantrip with your hex gun, add your Charisma modifier to the damage it deals on a hit (if you don't already add your Charisma modifier to it).
Bullet Hell
Prerequisite: 5th level, Pact of the Trigger feature (revolver form)
As an action, you temporarily duplicate your hex gun to unleash a flurry of bullets. All creatures within a 15-foot
cone in front of you must succeed a Dexterity saving throw against your spell save DC or take 2d10 force damage. This damage increases to 3d10 at 11th level and 4d10 at 17th level. To use this bonus action, you need to be holding your hex gun in one hand and have the other hand free.
You can use this invocation a number of times equal to your Charisma modifier (minimum of once), and you
regain all expended uses when you finish a short or long rest.
Crippling Shot
Prerequisite: Pact of the Trigger feature (revolver form)
Once on each of your turns when you damage a creature with an attack made using your hex gun, you can force it to make a Strength saving throw against your spell save DC or fall prone and have its speed reduced to 0 until the start of your next turn.
You can use this invocation a number of times equal to your Charisma modifier (minimum of once), and you regain all expended uses when you finish a long rest.
Dead Eye
Prerequisite: 15th level, Pact of the Trigger feature (sniper form)
If you haven't moved this turn, you can take aim as a bonus action, reducing your speed to 0 and granting you advantage on all attacks you make using your hex gun until the end of your turn.
Headshots
Prerequisite: 9th level, Pact of the Trigger feature (sniper form)
As a bonus action, you can enhance your focus to see the weak spots of your foes. For the next minute, attacks you make using your hex gun score a critical hit on a roll of 19 or 20. Once you've used this invocation, you can't use it again until you finish a short or long rest.
Quickstep
Prerequisite: 7th level, Pact of the Trigger feature
Your reflexes are honed. As a reaction, when an enemy makes a melee attack against you, before being hit, if your speed isn't 0, you can move 5 feet away from the foe without triggering opportunity attacks, potentially avoiding the attack if you leave its range.
You can use this invocation a number of times equal to your Charisma modifier (minimum of once), and you regain all expended uses when you finish a long rest.
Ricochet
Prerequisite: 7th level, Pact of the Trigger feature
Until the end of your turn, you enhance your hex gun. When you hit a creature with a cantrip cast with your
hex gun, you can immediately cause the hit to wound a second creature within 15 feet of the original target. The second target takes damage (of the type of the cantrip) equal to your Charisma modifier (minimum 1).
You can use this invocation to enhance your hex gun a number of times equal to your Charisma modifier, and you regain all expended uses when you finish a short or long rest.
Riposte
Prerequisite: 7th level, Pact of the Trigger feature (revolver form)
When an enemy attacks you with a melee attack, you can fire a special bullet to counter it as a reaction before
being hit. Make a melee or ranged spell attack. On a hit, the enemy takes 1d10 force damage, its attack fails, and it is stunned until the end of its current turn.
Once you’ve used this invocation to damage an enemy, you can’t use it again until you finish a short or long rest.
