  We perform a lattice calculation on the radiative decay of $D_s^*$ using the
(2+1)-flavor Wilson-clover gauge ensembles generated by CLQCD collaboration. A
method allowing us to calculate the form factor with zero transfer momentum is
proposed and applied to the radiative transition $D_s^*\rightarrow D_s\gamma$
and the Dalitz decay $D_s^*\rightarrow D_s e^+e^-$. After a continuum
extrapolation using three lattice spacings, we obtain $\Gamma(D_s^*\rightarrow
D_s \gamma)=0.0549(54)$ keV, where the error is purely statistical. The result
is consistent with previous lattice calculations but with a error reduced to
only a fifth of the before. The Dalitz decay rate is also calculated for the
first time and the ratio with the radiative transition is found to be
$R_{ee}=0.624(3)\%$. A total decay width of $D_s^*$ can then be determined as
0.0587(54) keV taking into account the experimental branching fraction.
Combining with the most recent experimental measurement on the branching
fraction of the purely leptonic decay $D_s^{+,*}\rightarrow e^+\nu_e$, we
obtain the quantity
$f_{D_s^*}|V_{cs}|=(190.5^{+55.1}_{-41.7_{\textrm{stat.}}}\pm
12.6_{\textrm{syst.}})$ MeV, where the stat. is only the statistical error from
the experiment, and syst. results from the experimental systematic uncertainty
and the lattice statistical error. Our result leads to an improved systematic
uncertainty compared to $42.7_{\textrm{syst.}}$ obtained using previous lattice
prediction of total decay width $0.070(28)$ keV as the input.
