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: and with t→H^±b, H^±→W^±a, where a→μμ, in the mass ranges 15  GeV<m_a<72  GeV and 120  GeV≤m_H^±≤160  GeV.