We investigate the processes $e^+e^-$$to$$gamma J/psiphi$, $gamma J/psiomega$ and $pi^0 J/psieta$ to search for the charmnium-like states with hidden $sbar{s}$, such as $Y(4140)$, $Y(4274)$, $X(4350)$ and $X(3915)$. These processes will receive contributions from the charmed-strange meson rescatterings. When the center-of-mass energies of the $e^+e^-$ scatterings are taken around the $D_{s0}(2317)D_s^{*}$, $D_{s1}(2460)D_s$ or $D_{s1}(2460)D_s^{*}$ threshold, the anomalous triangle singularities can be present in the rescattering amplitudes, which implies a non-resonance explanation about the resonance-like structures. The positions of the anomalous triangle singularities are sensitive to the kinematics, which offers us a criterion to distinguish the kinematic singularities from genuine particles.
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