You cannot just shoot someone for simply trespassing nor can you point a gun at them otherwise you will likely be in trouble for threatening the trespasser with a gun.
You can however legally carry your gun on you or if you have a rifle then you may walk out your door and onto your property with your rifle but you cannot point the rifle at them while walking towards them.
You can only shoot someone for trespassing on your property if they're about to shoot you or harm you in anyway but you must retreat if possible.
Shooting someone simply for trespassing will land you in jail and prison.
You need to just call the cops and have them legally remove the trespasser if they will not leave and if they do return the trespasser will then be arrested.