A search is presented for new Higgs bosons in proton-proton (pp) collision events in which a same-sign top quark pair is produced in association with a jet, via the pp -> tH/ A -> tt (c) over bar and pp -> tH/ A -> tt<(u)over bar processes. Here, H and A represent the extra scalar and pseudoscalar boson, respectively, of the second Higgs doublet in the generalized two-Higgs-doublet model (g2HDM). The search is based on pp collision data collected at a center-of-mass energy of 13 TeV with the CMS detector at the LHC, corresponding to an integrated luminosity of 138 fb(-1). Final states with a same-sign lepton pair in association with jets and missing transverse momentum are considered. New Higgs bosons in the 200-1000GeV mass range and new Yukawa couplings between 0.1 and 1.0 are targeted in the search, for scenarios in which either H or A appear alone, or in which they coexist and interfere. No significant excess above the standard model prediction is observed. Exclusion limits are derived in the context of the g2HDM.