  In this article, the study of the orthogonality properties of $q$-polynomials
of the Hahn class started in the initial article by R. \'Alvarez-Nodarse, R.
Sevinik-Ad{\i}g\"uzel, and H. Ta\c{s}eli, \textit{On the orthogonality of
$q$-classical polynomials of the Hahn class I} is proceeded. To be more
specific, the orthogonality properties of the $q$-polynomials belonging to the
$\emptyset$-Hermite-Laguerre/Jacobi, $\emptyset$-Jacobi/Hermite-Laguerre,
0-Laguerre/Jacobi-Bessel and 0-Jacobi/Laguerre-Bessel cases are studied by
taking into account the idea considered in the initial paper. In particular, a
new orthogonality relation for the $q$-Meixner polynomials is established.
