This is a thing about your character which improves their use of a skill in a certain situation, so that's a character stunt. Perhaps...
There are many like her, but she's mine. You get +4 to attack with Shoot when using your personal sidearm.
That's a little overpowered for most versions of Fate Core, as the "bite" of the stunt (only using your personal sidearm) isn't likely to come up much. To make it better fit the typical stunt format I'd either change it to +2, or to weapon:4 (no bonus to the Shoot modifier, but inflicts +4 stress if the attack succeeds or ties). Run it past your group and see what they think!
If the bonus had been a quality of the gun itself, that'd have been a stunt attached to the gun, which anyone who picked up the gun could use:
Big Fancy Gun. This gun grants +2 when using Shoot to attack with it.
Or if your character is trained with really big guns:
Big Gun Training. You get +2 using Shoot to attack with guns that require both hands to pick up.
And if your character would technically be that good with any gun they picked up, but they only use really big guns, that'd be better expressed as putting a high rank into Shoot but also having a character aspect like A derringer broke my heart or Fat trigger finger and self-compelling it any time using a smaller gun would make your character's life easier.