  Using $e^+e^-$ annihilation data corresponding to an integrated luminosity of
6.32 fb$^{-1}$ collected at center-of-mass energies between 4.178 GeV and 4.226
GeV with the BESIII detector, we perform the first amplitude analysis of the
decay $D_s^+\to K_S^0K^+\pi^0$ and determine the relative branching fractions
and phases for intermediate processes. We observe the $a_0(1710)^+$, the
isovector partner of the $f_0(1710)$ and $f_0(1770)$ mesons, in its decay to
$K_S^0K^+$ for the first time. In addition, we measure the ratio
$\frac{\mathcal{B}(D_{s}^{+} \to
\bar{K}^{*}(892)^{0}K^{+})}{\mathcal{B}(D_{s}^{+} \to
\bar{K}^{0}K^{*}(892)^{+})}$ to be $2.35^{+0.42}_{-0.23\text{stat.}}\pm
0.10_{\rm syst.}$. Finally, we provide a precision measurement of the absolute
branching fraction $\mathcal{B}(D_s^+\to K_S^0K^+\pi^0) = (1.46\pm
0.06_{\text{stat.}}\pm 0.05_{\text{syst.}})\%$.
