  By investigating the very closely lied $D_{s1}\bar{D}_{s}+c.c.$ and
$D_{s0}\bar{D}^*_{s}+c.c.$ thresholds at about 4.43 GeV we propose that the
$\psi(4415)$ and $\psi(4160)$ can be mixing states between the dynamic
generated states of the strong $S$-wave $D_{s1}\bar{D}_{s}+c.c.$ and
$D_{s0}\bar{D}^*_{s}+c.c.$ interactions and the quark model states $\psi(4S)$
and $\psi(2D)$. We investigate the $J/\psi K\bar{K}$ final states and invariant
mass spectrum of $J/\psi K$ to demonstrate that nontrivial lineshapes can arise
from such a mechanism. This process, which goes through triangle loop
transitions, is located in the vicinity of the so-called "triangle singularity
(TS)" kinematics. As a result, it provides a special mechanism for the
production of exotic states $Z_{cs}$, which is the strange partner of
$Z_c(3900)$, but with flavor contents of $c\bar{c}q\bar{s}$ (or
$c\bar{c}s\bar{q}$) with $q$ denoting $u/d$ quarks. The lineshapes of the
$e^+e^-\to J/\psi K\bar{K}$ cross sections and $J/\psi K \ (J/\psi \bar{K})$
spectrum are sensitive to the dynamically generated state, and we demonstrate
that a pole structure can be easily distinguished from open threshold CUSP
effects if an exotic state is created. A precise measurement of the cross
section lineshapes can test such a mixing mechanism and provide navel
information for the exotic partners of the $Z_c(3900)$ in the charmonium
spectrum.
