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In this work, we investigate the interactions between the charmed-strangemeson ($D_s, D_s^{*}$) in $H$-doublet and the (anti-)charmed-strange meson($D_{s1}, D_{s2}^{*}$) in $T$-doublet, where the one boson exchange model isadopted by considering the $S$-$D$ wave mixing and the coupled-channel effects.By extracting the effective potentials for the discussed $H_s\bar{T}_s$ and$H_s{T}_s$ systems, we try to find the bound state solutions for thecorresponding systems. We predict the possible hidden-charm hadronic molecularstates with hidden strangeness, i.e., the $D_s^{*}\bar D_{s1}+c.c.$ states with$J^{PC}$=$0^{--}, 0^{-+}$ and the $D_s^{*}\bar D_{s2}^{*}+c.c.$ states with$J^{PC}$=$1^{--}, 1^{-+}$. Applying the same theoretical framework, we alsodiscuss the $H_s T_s$ systems. Unfortunately, the existence of the open-charmand open-strange molecular states corresponding to the $H_s T_s$ systems can beexcluded.

Exotic double-charm molecular states with hidden or open strangeness and around $4.5\sim 4.7$ GeV