How to clean a cellphone screen protector of finger prints?
there are washable screen protectors on the market. using a mild soap then running the screen protector through running water then let the screen protector air dry.
How to Clean Screen Protectors
How to Wash a Screen Protector
Use an anti-static dry cloth
A drop of water can help too (be careful not to get it onto the phone itself!).
A microfiber cleansing cloth and/or very small amount of eyeglass cleaning solution should work for stubborn fingerprints, but just a microfiber cleaning cloth should be enough in most situations.