In this research work, we investigate the uniqueness problems and distribution of zeroes of q-shift difference-differential polynomials of entire and meromorphic functions having zero order in the complex plane ₵ of the form 〖( f^n P(f) ∆_q (f))〗^((k)) and 〖(g^n P(g) ∆_q (g))〗^((k)), where P(f) is a polynomial with constant coefficients of degree m, which is given in Lemma 2.2 and ∆_q (f) is a q-difference operator defined as ∆_q (f)=f(qz+c)-f(qz), which share a small function φ(z),∞ CM. By considering the concept of weighted sharing introduced by I. Lahiri (Nagoya Math. J. 161 (2001), 193–206), we also investigate the uniqueness problem of q-shift difference-differential polynomials sharing a small function φ(z) with weight L, for the cases L≥2,L=1 and L=0 for a zero ordered entire functions. Our results improve, generalize, and extend earlier results due to Zhao and Zhang (J. Contemp. Math. Anal. 50 (2), 63–69). We have also given suitable examples to justify our results.