  We study the hadronic molecular states with the quark content
$bc\bar{s}\bar{q}$ by investigating the interactions of the $\bar{B}_s D$,
$\bar{B} D_s$, $\bar{B}_s^* D$, $\bar{B}^* D_s$, $\bar{B}_s D^*$, $\bar{B}
D_s^*$, $\bar{B}_s^* D^*$, and $\bar{B}^* D_s^*$ systems. By solving the
Bethe-Salpeter equation within the extended local hidden gauge formalism, we
find altogether six poles qualifying as possible hadronic molecular states: one
pole of $J^P=0^+$ below the $\bar{B}_s D$-$\bar{B}D_s$ threshold, one pole of
$J^P=1^+$ below the $\bar{B}_s^* D$-$\bar{B}^* D_s$ threshold, one pole of
$J^P=1^+$ below the $\bar{B}_s D^*$-$\bar{B}D_s^*$ threshold, and three poles
of $J^P=0^+/1^+/2^+$ below the $\bar{B}_s^* D^*$-$\bar{B}^* D_s^*$ threshold.
Their binding energies are calculated to be about 10-20 MeV with the cut-off
momentum $q_\textrm{max}=600\textrm{ MeV}$. Similarly, we study the hadronic
molecular states with $bs\bar{c}\bar{q}$ by investigating the interactions of
the $\bar{B}\bar{D}_s$, $\bar{B}_c\bar{K}$, $\bar{B}^*\bar{D}_s$,
$\bar{B}_c^*\bar{K}$, $\bar{B}\bar{D}_s^*$, $\bar{B}_c\bar{K}^*$,
$\bar{B}^*\bar{D}_s^*$, $\bar{B}_c^*\bar{K}^*$ systems, and the states with
$bq\bar{c}\bar{s}$ by investigating the interactions of the $\bar{B}_s\bar{D}$,
$\bar{B}_cK$, $\bar{B}_s^*\bar{D}$, $\bar{B}_c^*K$, $\bar{B}_s\bar{D}^*$,
$\bar{B}_cK^*$, $\bar{B}_s^*\bar{D}^*$, $\bar{B}_c^*K^*$ systems. However, no
deeply-bound poles are found in these systems.
