The aim of this article is to introduce the notion of Hom-Lie H-pseudo-superalgebras for any Hopf
algebra H. This class of algebras is
a natural generalization of the Hom-Lie pseudo-algebras as well as a special
case of the Hom-Lie superalgebras. We present some construction theorems of
Hom-Lie H-pseudo-superalgebras,
reformulate the equivalent definition of Hom-Lie H-pseudo-super-algebras, and consider the cohomology theory of Hom-Lie H-pseudo-superalgebras with coefficients
in arbitrary Hom-modules as a generalization of Kac’s result.
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