Emergence of molecular-type characteristic spectrum of hidden-charm pentaquark with strangeness embodied in the $P_{\psi s}^{\mathrm{\Lambda }}(4338)$ and $P_{cs}(4459)$

Inspired by the newly observed $P_{\psi s}^{\mathrm{\Lambda }}(4338)$ and the reported $P_{cs}(4459)$, we indicate the existence of the molecular-type characteristic mass spectrum for hidden-charm pentaquark with strangeness. It shows that the $P_{cs}(4459)$ may contain two substructures corresponding to the ${\mathrm{\Xi }}_c{\bar{D}}^{\ast }$ molecular states with $J^P=1\mathrm{/}{2}^{-}$ and $3\mathrm{/}{2}^{-}$, while there exists the corresponding ${\mathrm{\Xi }}_c\bar{D}$ molecular state with $J^P=1\mathrm{/}{2}^{-}$. As the prediction, we present another characteristic mass spectrum of the ${\mathrm{\Xi }}_c^{\mathrm{\prime }}{\bar{D}}^{(\ast )}$ molecular states. Experimental confirmation of these characteristic mass spectra is a crucial step of constructing hadronic molecular family.