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 Zcs^± in the decays Zcs^±→ K^±ψ(2S). No significant Zcs^± signals are observed.
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