Hadronic molecular states with the quark contents <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>b</mml:mi><mml:mi>c</mml:mi><mml:mover accent="true"><mml:mi>s</mml:mi><mml:mo stretchy="false">¯</mml:mo></mml:mover><mml:mover accent="true"><mml:mi>q</mml:mi><mml:mo stretchy="false">¯</mml:mo></mml:mover></mml:math> , <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>b</mml:mi><mml:mover accent="true"><mml:mrow><mml:mi>…

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