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We introduce S-modules, generalizing the notion of Krein $C^*$-modules, wherea fixed unitary replaces the symmetry of Krein $C^*$-modules. Therepresentation theory on S-modules is explored and for a given $*$-automorphism$\alpha$ on a $C^*$-algebra the KSGNS construction for $\alpha$-completelypositive maps is proved. An extention of this theorem for $\tau$-maps is alsoachieved, when $\tau$ is an $\alpha$-completely positive map, along with adecomposition theorem for $\mathfrak K$-families.

KSGNS construction for $\tau$-maps on S-modules and $\mathfrak{K}$-families