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The first search for a heavy neutral spin-1 gauge boson ((Formula presented)) with nonuniversal fermion couplings produced via vector boson fusion processes and decaying to tau leptons or (Formula presented) bosons is presented. The analysis is performed using LHC data at (Formula presented), collected from 2016 to 2018 with the CMS experiment and corresponding to an integrated luminosity of (Formula presented). The data are consistent with the standard model predictions. Upper limits are set on the product of the cross section for production of the (Formula presented) boson and its branching fraction to (Formula presented) or (Formula presented). The presence of a (Formula presented) boson decaying to (Formula presented) ((Formula presented)) is excluded for masses up to 2.45(1.60) TeV, depending on the (Formula presented) boson coupling to standard model weak bosons, and assuming a (Formula presented) ((Formula presented)) branching fraction of 50%.