We report the first measurement of the semileptonic decay $D_s^{+}\to K^{*}(892{)}^0{\mu }^{+}{\nu }_{\mu }$ and an improved measurement of the decay $D_s^{+}\to K^{*}(892{)}^0{e}^{+}{\nu }_e$ using a sample of $7.33{fb}^{-1}$ of $e^{+}{e}^{-}$ annihilation data collected at center-of-mass energies between 4.128 to 4.226~GeV with the BESIII detector at the BEPCII collider. We measure the branching fractions to be $\mathcal B({D^+_s\rightarrow K^*(892)^0 \mu^+\nu_{\mu}})=(2.07\pm0.22_{\rm stat}\pm0.10_{\rm syst})\times10^{-3}$ and $\mathcal B({D^+_s\rightarrow K^*(892)^0 e^+\nu_{e}})=(2.14\pm0.18_{\rm stat}\pm0.10_{\rm syst})\times10^{-3}$. Based on a simultaneous study of the dynamics in two semileptonic decays, the hadronic form factor parameters in the $D_s^{+}\to K^{*}(892{)}^0$ transition are determined to be $r_{V} = V(0)/A_1(0) = 1.63 \pm 0.14_{\rm stat} \pm 0.08_{\rm syst}$, $r_{2} = A_2(0)/A_1(0) = 0.60 \pm 0.13_{\rm stat} \pm 0.06_{\rm syst}$, and $A_1(0)=0.56 \pm 0.02_{\rm stat} \pm 0.01_{\rm syst}$, where $V(0)$ is the vector form factor and $A_{1,2}(0)$ are the axial-vector form factors evaluated at $q^2=0$. The precision of $r_V$ and $r_2$ is improved by twofold and $A_1(0)$ is measured for the first time. We also report the first model-independent measurements of the differential decay rates and the lepton forward-backward asymmetries for $D_s^{+}\to K^{*}(892{)}^0{\ell }^{+}{\nu }_{\ell }$ decays. Based on these measurements, we perform a test of lepton flavor universality in full and separate $q^2$ intervals with $D_s^{+}\to K^{*}(892{)}^0{\ell }^{+}{\nu }_{\ell }$ decays. No violation is found within uncertainties. Our results present for the first time a complete study of the dynamics in the $D_s^{+}\to K^{*}(892{)}^0$ transition, and provide stringent tests of various non-perturbative theoretical calculations.