More then likely, you’re bringing out the drill since it’s a clone controller and not an original where the screws are good quality. However, what may work to get them out is to go one size up from the factory bit size - I am assuming Phillips because it isn’t a Nintendo product which would use the tri-wing screw.
If you need to drill it out, what you need to do is use the smallest bit you can get away with to break the head off, but leave enough room to get the screw stem out with plyers once you open the controller. Don’t go too far otherwise you will likely never be able to put a screw in that hole again. With a controller like this, you may be able to recover the use of the screw hole in question.