  We perform an effective-field-theory-based coupled-channel analysis of the
recent BES III data on the $e^+e^-$ annihilation into the final state
$K^+(D_s^-D^{*0}+D_s^{*-}D^0)$ in a wide energy range and extract the poles
responsible for the formation of the $Z_{cs}(3982)$. We identify two scenarios
which provide a similar description of the experimental mass distributions but
result in utterly different predictions for the spin partners of the
$Z_{cs}(3982)$: although both scenarios are consistent with the $Z_{cs}$ as a
$SU(3)$ partner of the $Z_c(3900)$, the $Z_c(4020)$ appears naturally as a spin
partner of these states only in one of them (fit 1) while in the other (fit 2)
its nature has to be different. Also, the $Z_{cs}(3982)$ has a $J^{P}=1^+$ spin
partner near the $\bar D_s^* D^*$ threshold in fit 1, while no such state
exists in fit 2. We predict the $\bar{D}_s^*D^*$ invariant mass distribution in
the $J^{P}=1^+$ channel for the reaction $e^+e^-\to K^+D_s^{*-}D^{*0}$ and
argue that this line shape can be used to distinguish between the two scenarios
once data in this channel are available.
