We present a collection of finitely generated projective generators for the category of graded modules over a unital semigroup-graded ring. Consequences of the existence of such a collection, as well as other module-theoretic re-sults, will arise from more general constructions involving TTF classes inside Grothendieck categories. For instance, we obtain a description of the category of graded modules whose support lies within a given subset of the semigroup.