How do you remove screws that are stuck but not stripped?

How do you remove screws that are stuck but not stripped?

I’m trying to self-replace the joycon rail on the left joycon, and have run into a problem. The phillips-head screw on the rail is stuck on really hard, and will not spin no matter how hard I try pushing with my screwdriver. The screw is not stripped. How do I get the screw out without damaging the electronic parts?