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We suggest to study the $B_{s}$ and its excitations $B_{sJ}$ in the $B_c$decays. We calculate the $B_c\to B_{sJ}$ and $B_c\to B_{J}$ form factors withinthe covariant light-front quark model, where the $B_{sJ}$ and $B_{J}$ denote ans-wave or p-wave $\bar bs$ and $\bar bd$ meson, respectively. The form factorsat $q^2=0$ are directly computed while their $q^2$-distributions are obtainedby the extrapolation. The derived form factors are then used to studysemileptonic $B_c\to (B_{sJ},B_{J})\bar\ell\nu$ decays, and nonleptonic $B_c\toB_{sJ}\pi$. Branching fractions and polarizations are predicted in the standardmodel. We find that the branching fractions are sizable and might be accessibleat the LHC experiment and future high-energy $e^+e^-$ colliders with a highluminosity at the $Z$-pole. The future experimental measurements are helpful tostudy the nonperturbative QCD dynamics in the presence of a heavy spectator andalso of great value for the spectroscopy study.

$B_c\to B_{sJ}$ form factors and $B_c$ decays into $B_{sJ}$ in covariant light-front approach