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The first four-dimensional amplitude analysis of the B+ → ψ(2S)K0Sπ+ decay is performed with proton-proton collision data collected by the LHCb experiment at √s = 13 TeV, corresponding to an integrated luminosity of 5.4 fb−1. The data cannot be fully explained by B+ → ψ(2S)K*+ contributions alone. A significantly better description of the data is obtained by adding a T+cc contribution decaying to ψ(2S)π+. The properties of the T+cc structure are consistent with the exotic state Tcc1(4430)+ reported in the isospin-related B0 → ψ(2S)K−π+ decay. Effects of a possible Tcc1(4430)+ → D*1 (2600)0D+ decay mode on the Tcc1(4430)+ → ψ(2S)π+ mass distribution are investigated through a Flatté parametrization, providing constraints on the relative decay strength. A description of the Tcc1(4430)+ structure using the triangle singularity mechanism is studied and also found to be consistent with the data.