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The strong decays of $D^\star_{s1}(2700)^\pm$ and $D^\star_{sJ}(2860)^\pm$are investigated within the $^3P_0$ model. It is found that the interpretationof these two states depends on the mixing schemes and the ways of choices ofthe harmonic oscillator parameter $\beta$. If $D^\star_{s1}(2700)^\pm$ and$D^\star_{sJ}(2860)^\pm$ are two pure states, $D^\star_{s1}(2700)^\pm$ seemsimpossibly the $2^3S_1$ $D_s$, but may be the $1^3D_1$ $D_s$.$D^\star_{sJ}(2860)^\pm$ may be the $1^3D_3$. If there is mixing between the$2^3S_1$ and $1^3D_1$, $D^\star_{s1}(2700)^\pm$ may be the mixed $1^-$ statewith a small mixing angle in the case of a special $\beta$ for each meson, and$D^\star_{sJ}(2860)^\pm$ is the orthogonal partner of $D^\star_{s1}(2700)^\pm$;$D^\star_{s1}(2700)^\pm$ may also be the mixed $1^-$ state with a large mixingangle based on a universal $\beta$ for all mesons, and $D^\star_{sJ}(2860)^\pm$seems impossibly the orthogonal partner of $D^\star_{s1}(2700)^\pm$. Otheruncertainties related to the choices of constituent quark masses and phasespaces are also explored.

$D^\star_{s1}(2700)^\pm$ and $D^\star_{sJ}(2860)^\pm$ revisited within the $^3P_0$ model