Using a data sample of 980 fb$^{-1}$ collected with the Belle detector at the KEKB asymmetric-energy $e^+e^-$ collider, we study the processes of $Xi^0_cto Lambdabar K^{*0}$, $Xi^0_cto Sigma^0bar K^{*0}$, and $Xi^0_cto Sigma^+K^{*-}$ for the first time. The relative branching ratios to the normalization mode of $Xi^0_ctoXi^-pi^+$ are measured to be $${cal B}(Xi^0_cto Lambdabar K^{*0})/{cal B}(xicto Xi^-pi^+)=0.18pm0.02({rm stat.})pm0.01({rm syst.}),$$ $${cal B}(Xi^0_cto Sigma^0bar K^{*0})/{cal B}(xicto Xi^-pi^+)=0.69pm0.03({rm stat.})pm0.03({rm syst.}),$$ $${cal B}(Xi^0_cto Sigma^+K^{*-})/{cal B}(xicto Xi^-pi^+)=0.34pm0.06({rm stat.})pm0.02({rm syst.}),$$ where the uncertainties are statistical and systematic, respectively. We obtain %measure the branching fractions of $Xi^0_cto Lambdabar K^{*0}$, $Xi^0_cto Sigma^0bar K^{*0}$, and $Xi^0_cto Sigma^+K^{*-}$ to be $${cal B}(Xi^0_cto Lambdabar K^{*0})=(3.3pm0.3({rm stat.})pm0.2({rm syst.})pm1.0({rm ref.}))times10^{-3},$$ $${cal B}(Xi^0_cto Sigma^0bar K^{*0})=(12.4pm0.5({rm stat.})pm0.5({rm syst.})pm3.6({rm ref.}))times10^{-3},$$ $${cal B}(Xi^0_cto Sigma^+K^{*-})=(6.1pm1.0({rm stat.})pm0.4({rm syst.})pm1.8({rm ref.}))times10^{-3},$$ where the uncertainties are statistical, systematic, and from ${cal B}(xic to Xi^-pi^+)$, respectively. The asymmetry parameters $alpha(Xi^0_cto Lambdabar K^{*0})$ and $alpha(Xi^0_cto Sigma^+K^{*-})$ are $0.15pm0.22({rm stat.})pm0.04({rm syst.})$ and $-0.52pm0.30({rm stat.})pm0.02({rm syst.})$, respectively, where the uncertainties are statistical followed by systematic.
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