  We search for $CP$ violation by measuring a $T$-odd asymmetry in the
Cabibbo-suppressed $D^{+}\rightarrow K^{+}K^{0}_{S}\pi^{+}\pi^{-} $ decay, and
in the Cabibbo-favored $D^{+}_{s}\rightarrow K^{+}K^{0}_{S}\pi^{+}\pi^{-}$ and
$D^{+}\rightarrow K^{+}K^{-}K^{0}_{S}\pi^{+}$ decays. We use 980 ${\rm
fb}^{-1}$ of data collected by the Belle detector running at the KEKB
asymmetric-energy $e^{+}e^{-}$ collider. The $C\!P$-violating $T$-odd parameter
${a}^{T\text{-}\rm{odd}}_{CP}$ is measured to be
${a}^{T\text{-}\rm{odd}}_{CP}(D^{+}\rightarrow
K^{+}K^{0}_{S}\pi^{+}\pi^{-})=(0.34\pm0.87\pm0.32)\%,$
${a}^{T\text{-}\rm{odd}}_{CP}(D^{+}_{s}\rightarrow
K^{+}K^{0}_{S}\pi^{+}\pi^{-})=(-0.46\pm0.63\pm0.38)\%,$ and
${a}^{T\text{-}\rm{odd}}_{CP}(D^{+}\rightarrow
K^{+}K^{-}K^{0}_{S}\pi^{+})=(-3.34\pm2.66\pm0.35)\%,$ where the first
uncertainty is statistical and the second is systematic. We also report the
first observation of the Cabibbo-suppressed decay $D^{+}_{s}\rightarrow
K^{+}K^{-}K^{0}_{S}\pi^{+}$. The branching fraction is measured relative to
that of the analogous Cabibbo-favored decay : $B(D^{+}_{s}\rightarrow
K^{+}K^{-}K^{0}_{S}\pi^{+}) / B(D^{+}_{s}\rightarrow
K^{+}K^{0}_{S}\pi^{+}\pi^{-}) = (1.36\pm 0.15\pm 0.04)\%$.
