Abstract This paper presents a search for direct top squark pair production in events with missing transverse momentum plus either a pair of jets consistent with Standard Model Higgs boson decay into b -quarks or a same-flavour opposite-sign dilepton pair with an invariant mass consistent with a Z boson. The analysis is performed using the proton–proton collision data at $$\sqrt{s}=13$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msqrt> <mml:mi>s</mml:mi> </mml:msqrt> <mml:mo>=</mml:mo> <mml:mn>13</mml:mn> </mml:mrow> </mml:math> TeV collected with the ATLAS detector during the LHC Run-2, corresponding to an integrated luminosity of 139 fb $$^{-1}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mrow/> <mml:mrow> <mml:mo>-</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msup> </mml:math> . No excess is observed in the data above the Standard Model predictions. The results are interpreted in simplified models featuring direct production of pairs of either the lighter top squark ( $$\tilde{t}_1$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mover> <mml:mi>t</mml:mi> <mml:mo>~</mml:mo> </mml:mover> <mml:mn>1</mml:mn> </mml:msub> </mml:math> ) or the heavier top squark ( $$\tilde{t}_2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mover> <mml:mi>t</mml:mi> <mml:mo>~</mml:mo> </mml:mover> <mml:mn>2</mml:mn> </mml:msub> </mml:math> ), excluding at 95% confidence level $$\tilde{t}_1$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mover> <mml:mi>t</mml:mi> <mml:mo>~</mml:mo> </mml:mover> <mml:mn>1</mml:mn> </mml:msub> </mml:math> and $$\tilde{t}_2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mover> <mml:mi>t</mml:mi> <mml:mo>~</mml:mo> </mml:mover> <mml:mn>2</mml:mn> </mml:msub> </mml:math> masses up to about 1220 and 875 GeV, respectively.