  The observed resonance peak around 2.86 GeV has been carefully reexamined by
the LHCb collaboration and it is found that under the peak there reside two
states $D^*_{s1}(2860)$ and $D^*_{s3}(2860)$ which are considered as
$1^3D_1(c\bar s)$ and $1^3D_3(c\bar s)$ with slightly different masses and
total widths. Thus, the earlier assumption that the resonance $D^*_{s1}(2710)$
was a $1D$ state should not be right. We suggest to measure the partial widths
of radiative decays of $D^*_{sJ}(2860)$ and $D^*_{s1}(2710)$ to confirm their
quantum numbers. We would consider $D^*_{s1}(2710)$ as $2^3S_1$ or a pure
$1^3D_1$ state, or their mixture and respectively calculate the corresponding
branching ratios as well as those of $D^*_{sJ}(2860)$. The future precise
measurement would provide us information to help identifying the structures of
those resonances .
