  By assuming that Y(4260) either is a $D_1\bar{D}$ molecular state, or has
sizeable couplings with $D_0 \bar{D}^*$ and $D_1^\prime \bar{D}$, we
investigate several decay modes of Y(4260). Under the special kinematic
configurations, triangle singularity (TS) may occur in the rescattering
amplitude, which will significantly change the threshold behavior. Obvious
threshold enhancements or narrow cusp structures appear quite naturally without
introducing a genuine resonance. We emphasize that the radiative decay modes
may be useful for studying $D^{(*)}\bar{D}$ $S$-wave scattering.
