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Utilizing a data set corresponding to an integrated luminosity of 6.32~$\rmfb^{-1}$, recorded by the BESIII detector at center-of-mass energies between4.178 and 4.226~GeV, we perform an amplitude analysis of the decay $D_{s}^{+}\to K_{S}^{0}\pi^{+}\pi^{0}$ and determine the relative fractions and phasedifferences of different intermediate processes, which include$K_{S}^{0}\rho(770)^{+}$, $K_{S}^{0}\rho(1450)^{+}$, $K^{*}(892)^{0}\pi^{+}$,$K^{*}(892)^{+}\pi^{0}$, and $K^{*}(1410)^{0}\pi^{+}$. Using a double-tagtechnique, and making an efficiency correction that relies on our knowledge ofthe phase-space distribution of the decays coming from the amplitude analysis,  the absolute branching fraction is measured to be $\mathcal{B}(D_{s}^{+} \toK_{S}^{0}\pi^{+}\pi^{0})=(5.43\pm0.30_{\text{stat}}\pm0.15_{\text{syst}})\times 10^{-3}$.

Amplitude analysis and branching-fraction measurement of \boldmath $D_{s}^{+} \to K^0_{S}\pi^{+}\pi^{0}$