  The mass and pole residue of the ground and first radially excited $
\Omega_c^{0}$ states with spin-parities $J^{P}=1/2^{+},\,3/2^{+}$, as well as
P-wave $\Omega_c^{0}$ with $J^{P}=1/2^{-},\,3/2^{-}$ are calculated by means of
the two-point QCD sum rules. The strong decays of $\Omega_c^{0}$ baryons are
also studied and width of these decay channels are computed. The relevant
computations are performed in the context of the full QCD sum rules on the
light-cone. Obtained results for the masses and widths are confronted with
recent experimental data of LHCb Collaboration, which allow us to interpret
$\Omega_c(3000)^{0}$, $\Omega_c(3050)^{0}$, and $ \Omega_c(3119)^{0} $ as the
excited $css$ baryons with the quantum numbers $ (1P,\,1/2^{-})$,
$(1P,\,3/2^{-})$, and $(2S,\,3/2^{+})$, respectively. The $ (2S,\,1/2^{+})$
state can be assigned either to $\Omega_c(3066)^{0}$ state or
$\Omega_c(3090)^{0}$ excited baryon.
