  In this paper, we provide a family of generalized discrete $q$-Hermite II
polynomials denoted by $\tilde{h}_{n,\alpha}(x,y|q)$. An explicit relations
connecting them with the $q$-Laguerre and Stieltjes-Wigert polynomials are
obtained. Summation formula is derived by using different analytical means on
their generating functions.
