How to hang a projector screen (cloth) with a few inches away from the wall?
I would fasten a "furring strip" (a piece of perhaps 2x2) to the wall at the top of the screen. Make it the same width as the screen, but screw it into the studs inside the wall (NOT just into the drywall sheet-rock)  Then hang the screen from that.

I would paint the strip black before installation to minimize visual interference. Depending on what kind of screen you are talking about (not disclosed?) you could put another identical strip at the bottom and actually STRETCH the screen fabric between the top "rail" and the bottom "rail". That would keep it nice and tight and wrinkle-free.