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Using (2.712±0.014)×109 ψ(3686) events collected with the BESIII detector operating at the BEPCII, we find an evidence of the ηc(2S)→K+K−η′ decay with a statistical significance of 3.1σ. Its decay branching fraction is measured to be (12.24±4.60(stat.)±2.37(syst.)±4.68(extr.))×10−4, where the first uncertainty is statistical, the second is systematic, and the third uncertainty is from the branching fraction of the ψ(3686)→γηc(2S) decay. The upper limit on the product branching fraction B[ψ(3686)→γηc(2S)]× B[ηc(2S)→K+K−η′] is set to be 1.14×10−6 at 90% confidence level. In addition, the branching fractions of χc1→K+K−η′ and χc2→K+K−η′ are updated to be (8.47±0.09(stat.)±0.47(syst.))×10−4 and (1.53±0.04(stat.)±0.08(syst.))×10−4, respectively. The precision is improved by twofold.