  In this paper, the authors deal with the $q$-Genocchi numbers and polynomials
with weight zero. They discover some interesting relations via the $p$-adic
$q$-integral on $\mathbb{Z}_{p}$ and familiar basis Bernstein polynomials.
Finally, the authors show that the $p$-adic $\log$ gamma functions are
associated with the $q$-Genocchi numbers and polynomials with weight zero.
