A search for a new pseudoscalar a-boson produced in events with a top-quark pair, where the a-boson decays into a pair of muons, is performed using s=13 TeV pp collision data collected with the ATLAS detector at the LHC, corresponding to an integrated luminosity of 139 fb-1. The search targets the final state where only one top quark decays to an electron or muon, resulting in a signature with three leptons eμμ and μμμ. No significant excess of events above the Standard Model expectation is observed and upper limits are set on two signal models: pp→tt¯a and pp→tt¯ with t→H±b, H±→W±a, where a→μμ, in the mass ranges 15 GeV<ma<72 GeV and 120 GeV≤mH±≤160 GeV.