  A search for $\textit{CP}$ violation in $D^{0} \rightarrow K_{S}^{0} K^{+}
\pi^{-} $ and $D^{0} \rightarrow K_{S}^{0} K^{-} \pi^{+} $ decays is reported.
The search is performed using an unbinned model-independent method known as the
energy test that probes local $\textit{CP}$ violation in the phase space of the
decays. The data analysed correspond to an integrated luminosity of
$5.4~$fb$^{-1}$ collected in proton-proton collisions by the LHCb experiment at
a centre-of-mass energy of $\sqrt{s}=13$~TeV, amounting to approximately 950
thousand and 620 thousand signal candidates for the $D^{0} \rightarrow
K_{S}^{0} K^{-} \pi^{+} $ and $D^{0} \rightarrow K_{S}^{0} K^{+} \pi^{-} $
modes, respectively. The method is validated using $D^{0} \rightarrow K^{-}
\pi^{+} \pi^{-} \pi^{+} $ and $D^{0} \rightarrow K_{S}^{0} \pi^{+} \pi^{-} $
decays, where $\textit{CP}$-violating effects are expected to be negligible,
and using background-enhanced regions of the signal decays. The results are
consistent with $\textit{CP}$ symmetry in both the $D^{0} \rightarrow K_{S}^{0}
K^{-} \pi^{+} $ and the $D^{0} \rightarrow K_{S}^{0} K^{+} \pi^{-} $ decays,
with $p$-values for the hypothesis of no $\textit{CP}$ violation of 70% and
66%, respectively.
