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