A search for supersymmetry involving the pair production of gluinos decaying via off-shell third-generation squarks into the lightest neutralino () is reported. It exploits LHC proton–proton collision data at a centre-of-mass energy √s=13 TeV with an integrated luminosity of 139 fb⁻¹ collected with the ATLAS detector from 2015 to 2018. The search uses events containing large missing transverse momentum, up to one electron or muon, and several energetic jets, at least three of which must be identified as containing b-hadrons. Both a simple kinematic event selection and an event selection based upon a deep neural-network are used. No significant excess above the predicted background is found. In simplified models involving the pair production of gluinos that decay via off-shell top (bottom) squarks, gluino masses less than 2.44 TeV (2.35 TeV) are excluded at 95% CL for a massless . Limits are also set on the gluino mass in models with variable branching ratios for gluino decays to , and .