  In this work, the $\Omega_c$-like molecular states are systematically
investigated in a quasipotential Bethe-Salpeter equation approach. The relevant
interactions $\Xi_c^{(*,')}\bar{K}^{(*)}$, $\Xi^{(*)}D^{(*)}$, and
$\Omega^{(*)}_c(\pi/\eta/\rho/\omega)$ are described by light meson exchanges
with the help of the effective Lagrangians with SU(3), chiral, and heavy quark
symmetries. The obtained potential kernels of considered interactions are
inserted into the quasipotential Bethe-Salpeter equation, and coupled-channel
calculations are performed to find possible molecular states and its couplings
to the channels considered. The results suggest that an isoscalar state can be
produced from the $\Xi^*_c\bar{K}$ interaction with spin parity $3/2^-$, which
can be related to state $\Omega_c(3120)$. And its isoscalar partner is
predicted with a dominant decay in the $\Omega_c^*\pi$ channel. The isoscalar
and isovector states with $1/2^-$ can be produced from the $\Xi'_c\bar{K}$
interaction with a threshold close to the mass of the $\Omega_c(3050)$ and
$\Omega_c(3065)$. Their couplings to the $\Xi_c \bar{K}$ channel are very weak,
and the isovector one has strong coupling to $\Omega_c\pi$. High precision
measurement is helpful to confirm or search such molecular states. Experimental
search of states with higher masses generated from interactions $\Xi^{(*,')}_c
\bar{K}^*$ and $\Xi^* D^{(*)}$ are also suggested by the current results.
