Without seeing you shoot it's hard to answer that. Have you tried shooting on a bench or something that you can steady the gun and you to see where it's shooting? It's not often the sights on a fixed sight pistol are off.
Your off target most likely was not the gun but was the shooter.A left of center issue for a right handed shooter usually means you have too little finger on the trigger and are pushing the gun a little. If your left handed (like me) then it be too much finger causing a pull. Of course the right of center is just the opposite. A small flinch in any direction will look more pronounced the longer the distance you are from your target.
You can move the rear sight but you have to be careful not to ding up the sight when you're doing it.