We present the first search for the lepton-flavor-violating decay modes B0→KS0 \tau\pm \ell\mp (\ell=μ,e) using the 711 and 365 fb-1 data samples recorded by the Belle and Belle II detectors, respectively. We use a hadronic B-tagging technique to fully reconstruct a B meson and search for signal decays in the system recoiling against the tagged meson, considering \tau decays to either light leptons, one charged hadron, or one charged hadron and a neutral pion. We find no evidence for B0→KS0 \tau\pm \ell\mp decays and set 90% confidence level upper limits on the branching fractions in the range of [0.8,3.6]×10-5.