  In this article, we take the $D_{s3}^*(2860)$ and $D_{s1}^*(2860)$ as the
$1^3{\rm D}_3$ and $1^3{\rm D}_1$ $c\bar{s}$ states, respectively, study their
strong decays with the heavy meson effective theory by including the chiral
symmetry breaking corrections. We can reproduce the experimental data ${\rm
Br}\left(D_{sJ}^*(2860)\to D^*K\right)/{\rm Br}\left(D_{sJ}^*(2860)\to D
K\right) =1.10 \pm 0.15 \pm 0.19$ with suitable hadronic coupling constants,
the assignment of the $D_{sJ}^*(2860)$ as the $D_{s3}^*(2860)$ is favored, the
chiral symmetry breaking corrections are large. Furthermore, we obtain the
analytical expressions of the decay widths, which can be confronted with the
experimental data in the future to fit the unknown coupling constants. The
predictions of the ratios among the decay widths can be used to study the decay
properties of the $D_{s3}^*(2860)$ and $D_{s1}^*(2860)$ so as to identify them
unambiguously. On the other hand, if the chiral symmetry breaking corrections
are small, the large ratio $R=1.10 \pm 0.15 \pm 0.19$ requires that the
$D_{sJ}^*(2860)$ consists of at least four resonances $D_{s1}^*(2860)$,
$D_{s2}^*(2860)$, $D_{s2}^{*\prime}(2860)$, $D_{s3}^*(2860)$.
