He wasn't really "making use of a firearm in the performance of his duties" but kinda. In the episode when the "Man With A Limp" shows up and Barney thinks he's going to harm Andy, Andy does have a gun handy--just in case. But he doesn't reveal it and the repentant ex-prisoner never knows it was there.
Although not shown, in this same ep, 'High Noon In Mayberry,' Barney mentions that Andy once shot Luke Comstock in the leg during a filling station robbery.
In Season 6, "Aunt Bee Gets a Job", Andy grabs Warren's gun and shoots out a tire as the counterfeiters tried to escape. And there was a fellow walking in the background in the direction of the shot, so Andy got a little reckless there! Had Barney been around there would have been ample warnings to "watch out for the flying lead!"
All Aunt Bee could say was "Well, just because they are going out of business is no reason to shoot at them!"
In the ep where Barney swallows his gum while in the barn, Andy has both a revolver and a rifle plus the walkie-talkie. I think? Have to go watch that one again.