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We perform the first investigation of the process e+e−→K+K−ψ(2S) and report its Born cross sections over a range of center-of-mass energies from 4.699 to 4.951~GeV. The measurements are carried out using several partial reconstruction techniques using data samples collected by the BESIII detector with a total integrated luminosity of 2.5~fb−1. We search for new tetraquark candidates Z±cs in the decays Z±cs→K±ψ(2S). No significant Z±cs signals are observed.