Observation of the $W$-Annihilation Decay $D^{+}_{s} \rightarrow \omega \pi^{+}$ and Evidence for $D^{+}_{s} \rightarrow \omega K^{+}$

We report on the observation of the $W$-annihilation decay $D^{+}_{s} \rightarrow \omega \pi^{+}$ and the evidence for $D_{s}^{+} \rightarrow \omega K^{+}$ with a data sample corresponding to an integrated luminosity of 3.19 fb$^{-1}$ collected with the BESIII detector at the center-of-mass energy $\sqrt{s} = 4.178$ GeV. We obtain the branching fractions $\mathcal{B}(D^{+}_{s} \rightarrow \omega \pi^{+}) = (1.77\pm0.32_{{\rm stat.}}\pm0.11_{{\rm sys.}}) \times 10^{-3}$ and $\mathcal{B}(D^{+}_{s} \rightarrow \omega K^{+}) = (0.87\pm0.24_{{\rm stat.}}\pm0.07_{{\rm sys.}}) \times 10^{-3}$, respectively.