What affect do gamma rays have on charge or mass of the nucleus?

Gamma ray is not a particle. It is an electromagnetic wave so has no effect at all

Emitting gamma rays has no effect on the charge and the mass number.

they dont have an affect

Actually, I do not agree with the previous replies. There are exotic reactions where gamma rays affect the nucleus. These are a special class of reactions called photonuclear reactions. For instance, if you impinge a beam of gamma rays with well-defined energy the nucleus can absorb it and emit either one (gamma-n reaction) or two neutrons (gamma-2n reaction). This is a brief answer but there is a lot more detail to it. Furthermore, emitting neutrons from the nucleus obviously changes the mass thereof. The shorthand for these reactions is: