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In this paper, we discuss new results related to the generalized discrete q-Hermite II polynomialsh n,α (x; q), introduced by Mezlini et al. in 2014. Our aim is to give a continuous orthogonality relation, a q-integral representation and an evaluation at unity of the Poisson kernel, for these polynomials. Furthermore, we introduce q-Schrödinger operators and give the raising and lowering operator algebra corresponding to these polynomials. Our results generate a new explicit realization of the quantum algebra su q (1, 1), using the generators associated with a q-deformed generalized para-Bose oscillator. keywords: q-orthogonal polynomials, q-deformed algebras, harmonic oscillators. MSC(2010): 33D45; 81R30; 81R50.

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