Supergeometry is part and parcel of many classical and quantum field theories involving odd fields, e.g., SUSY field theory, BRST theory, or supergravity.
In particular, superconnections are defined as Koszul connections on these modules and sheaves.
However, supergeometry is not particular noncommutative geometry because of a different definition of a graded derivation.
Graded manifolds are characterized by sheaves on smooth manifolds, while supermanifolds are constructed by gluing of sheaves of supervector spaces.
In particular, supervector bundles and principal superbundles are considered in the category of
These superconnections have been applied to computing the Chern character in K-theory, noncommutative geometry, and BRST formalism.