Let R be an associative ring with identity, and Y be a class of right R -modules,
which contains all injective right R -modules. In this paper, we introduce the definition of
Y -Gorenstein cotorsion modules, which is a generalization of cotorsion and Gorenstein
cotorsion modules. We discuss the relationship between Gorenstein cotorsion, weakly
Gorenstein cotorsion and Y -Gorenstein cotorsion modules. We investigate properties and
characterizations of Y-Gorenstein cotorsion modules.