Searches are presented for direct production of top or bottom squark pairs in proton–proton collisions at the CERN LHC. Two searches, based on complementary techniques, are performed in all-jet final states that are characterized by a significant imbalance in transverse momentum. An additional search requires the presence of a charged lepton isolated from other activity in the event. The data were collected in 2015 at a centre-of-mass energy of 13 TeV with the CMS detector and correspond to an integrated luminosity of 2.3 fb⁻¹. No statistically significant excess of events is found beyond the expected contribution from standard model processes. Exclusion limits are set in the context of simplified models of top or bottom squark pair production. Models with top and bottom squark masses up to 830 and 890 GeV, respectively, are probed for light neutralinos. For models with top squark masses of 675 GeV, neutralino masses up to 260 GeV are excluded at 95% confidence level.