A search for charge-parity (CP) violation in Cabibbo-suppressed D_{s}^{+}→K_{S}^{0}π^{+}, D^{+}→K_{S}^{0}K^{+}, and D^{+}→ϕπ^{+} 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 areA_{CP}(D_{s}^{+}→K_{S}^{0}π^{+})=(1.3±1.9±0.5)×10^{-3},A_{CP}(D^{+}→K_{S}^{0}K^{+})=(-0.09±0.65±0.48)×10^{-3},A_{CP}(D^{+}→ϕπ^{+})=(0.05±0.42±0.29)×10^{-3},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. A combination with previous LHCb measurements, based on data collected at 7 and 8 TeV, is also reported.