Representations and cohomologies of Hom-δ-Jordan Lie supertriple systems are established. As an application, Nijenhuis operators and abelian extensions of Hom-δ-Jordan Lie supertriple systems are discussed. We obtain the infinitesimal deformation generated by virtue of a Nijenhuis operator. It is obtained that the sufficient and necessary condition for the equivalence of abelian extensions of Hom-δ-Jordan Lie supertriple systems.