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With the motivation of determining its further properties, which can be observed in experiments, we now present a calculation of the decay processes of this $K^*$, namely $K^*(4307)$, to two-body channels. Particularly, we consider the decay channels $J/\\psi K^*(892)$, $\\bar{D}D_s$, $\\bar{D}D_s^*$ and $\\bar{D}^* D_s^*$. 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