  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.
