  In this contribution we consider sequences of monic polynomials orthogonal
with respect to a Sobolev-type inner product \[ \langle f,g \rangle _{S}:=
\langle {\bf u}, f g\rangle +N (\mathscr D_q f)(\alpha) (\mathscr D
_{q}g)(\alpha),\qquad \alpha\in \mathbb R, \quad N\ge 0, \] where $\bf u$ is a
$q$-classical linear functional and $\mathscr D _{q}$ is the $q$-derivative
operator.
  We obtain some algebraic properties of these polynomials such as an explicit
representation, a five-term recurrence relation as well as a second order
linear $q$-difference holonomic equation fulfilled by such polynomials.
  We present an analysis of the behaviour of its zeros function of the mass
$N$. In particular, we in the exact values of $N$ such that the smallest
(respectively, the greatest) zero of the studied polynomials is located outside
of the support of the measure.
  We conclude this work considering two examples.
