  We investigate the angular decay distribution of the four-fold $B_{c}\to
D^{\ast}_{s}(\to D_{s}\gamma)\mu^{+}\mu^{-}$, and $B_{c}\to D^{\ast}_{s}(\to
D_{s}\pi)\mu^{+}\mu^{-}$ decays that proceed through $b\to s\mu^{+}\mu^{-}$
quark level transition. We use the model independent effective Hamiltonian with
vector and axial vector new physics operators to formulate the angular
observables and study the implications of different latest new physics
scenarios, taken from the global fits to all the $b\to s$ data, on these
observables. We also give Standard Model and new physics predictions of several
observables such as differential branching ratios, forward backward asymmetry,
longitudinal polarization fraction of $D_s^{\ast}$, and the unpolarized and
polarized lepton flavor universality violating ratios. Future measurements of
the predicted angular observables, both at current and future high energy
colliders, will add to the useful complementary data required to clarify the
structure of new physics in $b\to s\ell\ell$ neutral current decays.
