  A search for charge-parity ($CP$) violation in Cabibbo-suppressed $D_s^+\to
K_S^0 \pi^+$, $D^+\to K_S^0 K^+$ and $D^+\to \phi \pi^+$ decays is reported
using proton-proton collision data, corresponding to an integrated luminosity
of 3.8 fb$^{-1}$, collected at a center-of-mass energy of 13 TeV with the LHCb
detector. High-yield samples of kinematically and topologically similar
Cabibbo-favored $D_{(s)}^+$ decays are analyzed to subtract nuisance
asymmetries due to production and detection effects, including those induced by
$CP$ violation in the neutral kaon system. The results are \begin{align*}
\mathcal{A}_{CP}(D_s^+\to K_S^0 \pi^+)
&=\left(\phantom{-}1.3\phantom{0}\pm1.9\phantom{0}\pm0.5\phantom{0}\right)\times10^{-3},\\
\mathcal{A}_{CP}(D^+\to K_S^0 K^+)
&=\left(-0.09\pm0.65\pm0.48\right)\times10^{-3},\\ \mathcal{A}_{CP}(D^+\to \phi
\pi^+) &=\left(\phantom{-}0.05\pm0.42\pm0.29\right)\times10^{-3}, \end{align*}
where the first uncertainties are statistical and the second systematic. They
are the most precise measurements of these quantities to date, and are
consistent with $CP$ symmetry.
