  We study braiding statistics between quasiparticles and vortices in
two-dimensional charge-$2m$ (in units of $e$) superconductors that are coupled
to a $\mathbb Z_{2m}$ dynamical gauge field, where $m$ is any positive integer.
We show that there exist $16m$ types of braiding statistics when $m$ is odd,
but only $4m$ types when $m$ is even. Based on the braiding statistics, we
obtain a classification of topological phases of charge-$2m$
superconductors---or formally speaking, a classification of symmetry-protected
topological phases, as well as invertible topological phases, of
two-dimensional gapped fermions with $\mathbb Z_{2m}^f$ symmetry.
Interestingly, we find that there is no nontrivial fermionic symmetry-protected
topological phase with $\mathbb Z_4^f$ symmetry.
