  Stimulated by the new evidence of Y(4274) observed in the $J/\psi\phi$
invariant mass spectrum, we first propose the charmonium-like state Y(4274) as
the S-wave $D_s\bar{D}_{s0}(2317)+h.c.$ molecular state with $J^P=0^-$, which
is supported well by dynamics study of the system composed of the pseudoscalar
and scalar charmed mesons. The S-wave $D\bar{D}_{0}(2400)+h.c.$ molecular
charmonium appears as the molecular partner of Y(4274), which is in accord with
the enhancement structure appearing at 4.2 GeV in the $J/\psi\omega$ invariant
mass spectrum from B decays. Our study shows that the enhancement structures,
$i.e.$, the newly observed Y(4274) and the previously announced
$Y(4140)/Y(3930)$ in the $J/\psi\phi$ and $J/\psi\omega$ invariant mass
spectra, can be understood well under the uniform framework of the molecular
charmonium, which can be tested by future experiments.
