  The first observation of the singly Cabibbo-suppressed
$\Omega_{c}^{0}\to\Omega^{-}K^{+}$ and $\Omega_{c}^{0}\to\Xi^{-}\pi^{+}$ decays
is reported, using proton-proton collision data at a center-of-mass energy of
$13\,{\rm TeV}$, corresponding to an integrated luminosity of $5.4\,{\rm
fb}^{-1}$, collected with the LHCb detector between 2016 and 2018. The
branching fraction ratios are measured to be
$\frac{\mathcal{B}(\Omega_{c}^{0}\to\Omega^{-}K^{+})}{\mathcal{B}(\Omega_{c}^{0}\to\Omega^{-}\pi^{+})}=[6.08\pm0.51({\rm
stat})\pm0.40({\rm syst})]\%$,
$\frac{\mathcal{B}(\Omega_{c}^{0}\to\Xi^{-}\pi^{+})}{\mathcal{B}(\Omega_{c}^{0}\to\Omega^{-}\pi^{+})}=[15.81\pm0.87({\rm
stat})\pm0.44({\rm syst})\pm0.16({\rm ext})]\%$. In addition, using the
$\Omega_{c}^{0}\to\Omega^{-}\pi^{+}$ decay channel, the $\Omega_{c}^{0}$ baryon
mass is measured to be $M(\Omega_{c}^{0})=2695.28\pm0.07({\rm
stat})\pm0.27({\rm syst})\pm0.30({\rm ext})\,{\rm MeV}$, improving the
precision of the previous world average by a factor of 4.
