if its a flat head or phillips that the head is rusted so you cant even try to turn it then u will have to go drastic measures.......im thinking this is maybe a bathtub handle with the screw going into the stem holding it on? in that case you can break the handle off leaving the screw intact then remove the screw from the stem...if its broke flush with the stem just replace screw and stem.........occaisionally you maybe be able to cut a new slot in the head with a hacksaw.
You can also get a screw extractor or just drill it out and retap it....
If its a stem thats more work than its worth for me, i just go buy a new hdle and stem......
If you can find the stuff pictured below its the best stuff around.look at the name closely there are a lot of cheap chinese knockoffs that look just like it but are as effective as water.........