Summary: In this paper, we define the new families of Gauss \(k\)-Fibonacci polynomials. We obtain some exciting properties of the families. We give the relationships between the family of the Gauss \(k\)-Fibonacci polynomials and the known Gauss Fibonacci polynomials. We also define the generalized polynomials for these numbers. We also obtain some interesting properties of the polynomials. Furthermore, we Önd the new generalizations of these families and the polynomials in matrix representation. Then we prove Cassini’s identities for the families and their polynomials.