  For $0<\alpha\leq2$, a super-$\alpha$-stable motion $X$ in $\mathsf{R}^d$
with branching of index $1+\beta\in(1,2)$ is considered. Fix arbitrary $t>0$.
If $d<\alpha/\beta$, a dichotomy for the density function of the measure $X_t$
holds: the density function is locally H\"{o}lder continuous if $d=1$ and
$\alpha>1+\beta$ but locally unbounded otherwise. Moreover, in the case of
continuity, we determine the optimal local H\"{o}lder index.
