Parasupersymmetric quantum mechanics with generalized deformed parafermions

A superposition of bosons and generalized deformed parafermions corresponding to an arbitrary paraquantization order p is considered to provide deformations of parasupersymmetric quantum mechanics. New families of parasupersymmetric Hamiltonians are constructed in connection with two examples of su(2) nonlinear deformations such as introduced by Polychronakos and Ro\v cek