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Using data samples collected with the BESIII detector operating at the BEPCII storage ring at center-of-mass energies from 4.178 to 4.600 GeV, we study the process eþe− → π0Xð3872Þγ and search for Zcð4020Þ0 → Xð3872Þγ. We find no significant signal and set upper limits on σðeþe− → π0Xð3872ÞγÞ · BðXð3872Þ → πþπ−J=ψÞ and σðeþe− → π0Zcð4020Þ0Þ · BðZcð4020Þ0 → Xð3872ÞγÞ · BðXð3872Þ → πþπ−J=ψÞ for each energy point at 90% confidence level, which is of the order of several tenths pb.