  The notion of $q$-grading on the enveloping algebra generated by products of
q-deformed Heisenberg algebras is introduced for $q$ complex number in the unit
disc. Within this formulation, we consider the extension of the notion of
supersymmetry in the enveloping algebra. We recover the ordinary $\mathbb{Z}_2$
grading or Grassmann parity for associative superalgebra, and a modified
version of the usual supersymmetry. As a specific problem, we focus on the
interesting limit $q\to -1$ for which the Arik and Coon deformation of the
Heisenberg algebra allows to map fermionic modes to bosonic ones in a modified
sense. Different algebraic consequences are discussed.
