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A search is performed for dark matter produced in association with bottom quarks and a pair of electrons or muons in data collected with the CMS detector at the LHC, corresponding to 138 fb−1 of integrated luminosity of proton-proton collisions at a center-of-mass energy of 13 TeV. For the first time at the LHC, the associated production of a bottom quark-antiquark pair and a new heavy neutral Higgs boson (H) that subsequently decays into a leptonically decaying Z boson and a pseudoscalar (a) is explored. The latter acts as a dark matter mediator in the context of the two Higgs doublet model plus a pseudoscalar (2HDM+a). Multivariate techniques that target a wide range of mass configurations for the H and a particles are used. The observations are consistent with the expectations from standard model processes. Upper limits at 95% confidence level are set on the product of cross section and branching fraction of the new particles, ranging from 10−2 pb for an H mass of 400 GeV to 10−3 pb for an H mass of 2000 GeV. Constraints on the parameter space of a benchmark 2HDM+a model are derived and compared with expectations in the context of cosmological predictions.