Hidden and doubly heavy molecular states from interactions $D^{(*)}_{(s)}{\bar{D}}^{(*)}_{s}$/$B^{(*)}_{(s)}{\bar{B}}^{(*)}_{s}$ and ${D}^{(*)}_{(s)}D_{s}^{(*)}$/${B}^{(*)}_{(s)}B_{s}^{(*)}$

In this work, we perform a systematical investigation about the possible hidden and doubly heavy molecular states with open and hidden strangeness from interactions of $D^{(*)}{\bar{D}}^{(*)}_{s}$/$B^{(*)}{\bar{B}}^{(*)}_{s}$, ${D}^{(*)}_{s}{\bar{D}}^{(*)}_{s}$/${B}^{(*)}_{s}{\bar{B}}^{(*)}_{s}$, ${D}^{(*)}D_{s}^{(*)}$/${B}^{(*)}B_{s}^{(*)}$, and $D_{s}^{(*)}D_{s}^{(*)}$/$B_{s}^{(*)}B_{s}^{(*)}$ in a quasipotential Bethe-Salpeter equation approach. The interactions of the systems considered are described within the one-boson-exchange model, which includes exchanges of light mesons and $J/\psi/\Upsilon$ meson. Possible molecular states are searched for as poles of scattering amplitudes of the interactions considered. The results suggest that recently observed $Z_{cs}(3985)$ can be assigned as a molecular state of $D^*\bar{D}_s+D\bar{D}^*_s$, which is a partner of $Z_c(3900)$ state as a $D\bar{D}^*$ molecular state. The calculation also favors the existence of hidden heavy states $D_s\bar{D}_s/B_s\bar{B}_s$ with spin parity $J^P=0^+$, $D_s\bar{D}^*_s/B_s\bar{B}^*_s$ with $1^{+}$, and $D^*_s\bar{D}^*_s/B^*_s\bar{B}^*_s$ with $0^+$, $1^+$, and $2^+$. In the doubly heavy sector, the bound states can be found from the interactions $(D^*D_s+DD^*_s)/(B^*B_s+BB^*_s)$ with $1^+$, $D_s\bar{D}_s^*/B_s\bar{B}_s^*$ with $1^+$, $D^*D^*_s/B^*B^*_s$ with $1^+$ and $2^+$, and $D^*_sD^*_s/B^*_sB^*_s$ with $1^+$ and $2^+$. Some other interactions are also found attractive, but may be not strong enough to produce a bound state. The results in this work are helpful for understanding the $Z_{cs}(3985)$, and future experimental search for the new molecular states.