A search for heavy right-handed Majorana neutrinos is performed with the ATLAS detector at the CERN Large Hadron Collider, using the 140 fb-1 of proton–proton collision data at s=13 TeV collected during Run 2. This search targets tt¯ production, in which both top quarks decay into a bottom quark and a W boson, where one of the W bosons decays hadronically and the other decays into an electron or muon and a heavy neutral lepton. The heavy neutral lepton is identified through a decay into an electron or muon and another W boson, resulting in a pair of same-charge same-flavor leptons in the final state. This paper presents the first search for heavy neutral leptons in the mass range of 15–75 GeV using tt¯ events. No significant excess is observed over the background expectation, and upper limits are placed on the signal cross sections. Assuming a benchmark scenario of the phenomenological type-I seesaw model, these cross section limits are then translated into upper limits on the mixing parameters of the heavy Majorana neutrino with Standard Model neutrinos.