Using a data sample of (10087±44)×106 J/ψ events collected with the BESIII detector, we search for the decays η/η′→e+e−μ+μ− and η′→μ+μ−μ+μ− via the radiative decays J/ψ→γη/γη′. No excess of events over expected background is observed for any of the decays of interest. At 90% confidence level, we report the first upper limits on the branching fractions of η′→e+e−μ+μ− and η′→μ+μ−μ+μ− to be 1.75×10−6 and 5.28×10−7, respectively. In addition, we set an upper limit on the branching fraction of η→e+e−μ+μ− to be 6.88×10−6, which improves the previous result by about two orders of magnitude.