  In 2020, the LHCb collaboration reported the exclusive branching fractions
for the channels $B_s^0 \to D_s^{(*)-}\mu^+\nu_\mu$ for the very first time. In
view of these observations, we have recently reported the form factors and
branching fraction computations for these channels employing the covariant
confined quark model. As different other channels corresponding to $b \to c
\ell \nu_\ell$ have provided the hint for New Physics, the analysis of
observables such as forward-backward asymmetry, longitudinal and transverse
polarizations across the lepton flavours can serve as one of the important
probes for the search for possible New Physics. In present work, we compute
these observables for all the lepton flavours and compare our predictions with
the other theoretical approaches.
