When turning steering squeaks what could this be?

First check to make sure the fluid is topped off. If low there may be a leak in the system and you need to put fluid in the reservoir that has stop leak in it. If the problem continues then the pump is probably starting to go bad and you will want to replace it before it goes out. Last, Some Power Steering pumps just make noise and you have to deal with it. Do some research on your car and see if other people say the same thing. It is common for some makes/ models to have the same problems.