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A search for a new neutral gauge boson, Z′, produced in association with one or two jets, including at least one b jet, and decaying into a pair of muons is presented. The analysis uses proton-proton collision data collected with the CMS detector at s=13 TeV, corresponding to an integrated luminosity of 138 fb−1. No significant deviation from background expectations is observed. Upper limits at 95% confidence level on the product of cross section, branching fraction to dimuons, acceptance, and efficiency, from 0.2 to 2 fb, are set for Z′ boson masses between 125 and 350 GeV. Process-dependent products of acceptance and efficiency, and model-independent limits on the signal yield are provided. These are the only results to date in the 125–200 GeV mass range and the most stringent for b quark fusion production modes in the 200–350 GeV range, complementing inclusive Z′ boson searches.