We report the first search for a nonstandard-model resonance decaying into τ pairs in e^{+}e^{-}→μ^{+}μ^{-}τ^{+}τ^{-} events in the 3.6-10 GeV/c^{2} mass range. We use a 62.8 fb^{-1} sample of e^{+}e^{-} collisions collected at a center-of-mass energy of 10.58 GeV by the Belle II experiment at the SuperKEKB collider. The analysis probes three different models predicting a spin-1 particle coupling only to the heavier lepton families, a Higgs-like spin-0 particle that couples preferentially to charged leptons (leptophilic scalar), and an axionlike particle, respectively. We observe no evidence for a signal and set exclusion limits at 90% confidence level on the product of cross section and branching fraction into τ pairs, ranging from 0.7 to 24 fb, and on the couplings of these processes. We obtain world-leading constraints on the couplings for the leptophilic scalar model for masses above 6.5 GeV/c^{2} and for the axionlike particle model over the entire mass range.
