Hunting for the hidden-charm molecular states with strange quark in $B$ and $B_s$ decays

In the present work, we investigate the productions of the molecular states composed of $D_s^{(\ast )}{\bar{D}}^{(\ast )}$ and $D_s^{(\ast )}{\bar{D}}_s^{(\ast )}$ in the $B$ and $B_s$ decays by using an effective Lagrangian approach. The branching ratios in terms of the model parameter $\alpha$ and the binding energy $\mathrm{\Delta }E$ are estimated. Our estimations indicate that the branching fractions are of the order of ${10}^{-4}$ and the relative ratios are very weakly dependent on the model parameter $\alpha$ and the binding energy $\mathrm{\Delta }E$. The predicted ratios are helpful for searching the hidden-charm molecular states with strange quark in the future experiments at Belle II and LHCb.