Strange, are you at the lowest (biggest rear sprocket) or highest (smallest sprocket) gear? Is the chain length correct? In normal operation the rear mech cage shouldn't be anywhere near enough to touch the smallest cog irrespective of H screw adjustment.
The H screw is there to stop the mech from getting too far outboard, and only when you are on the highest gear (smallest rear sprocket), but it is only in play IF the cable is not taut then, otherwise the cable is functioning as the stop no matter how much you loosen the screw. For rear mech adjustment including H screw
this is as good a guide as any.