  In this article, we consider a weighted mean-field control problem with
jump-diffusion as its state process. The main difficulty is from the
non-Lipschitz property of the coefficients. We overcome this difficulty by an
$L_{p,q}$-estimate of the solution processes with a suitably chosen $p$ and
$q$. Convex pertubation method combining with the aforementioned
$L_{p,q}$-estimation method is utilized to derive the stochastic maximum
principle for this control problem. A sufficient condition for the optimality
is also given.
