A search for the pair production of the lightest supersymmetric partner of the top quark $\left({\tilde{t}}_1\right)$ $$ \left({\tilde{\mathrm{t}}}_1\right) $$ is presented. The search focuses on a compressed scenario where the mass difference between the top squark and the lightest supersymmetric particle, often considered to be the lightest neutralino $\left({\tilde{\chi }}_1^0\right)$ $$ \left({\tilde{\upchi}}_1^0\right) $$, is smaller than the mass of the W boson. The proton-proton collision data were recorded by the CMS experiment at a centre-of-mass energy of 13 TeV, and correspond to an integrated luminosity of 35.9 fb−1. In this search, two decay modes of the top squark are considered: a four-body decay into a bottom quark, two additional fermions, and a ${\tilde{\chi }}_1^0$ $$ {\tilde{\upchi}}_1^0 $$; and a decay via an intermediate chargino. Events are selected using the presence of a high-momentum jet, significant missing transverse momentum, and a low transverse momentum electron or muon. Two analysis techniques are used, targeting different decay modes of the ${\tilde{t}}_1$ $$ {\tilde{\mathrm{t}}}_1 $$: a sequential selection and a multivariate technique. No evidence for the production of top squarks is found, and mass limits at 95% confidence level are set that reach up to 560 GeV, depending on the $m\left({\tilde{t}}_1\right)-m\left({\tilde{\chi }}_1^0\right)$ $$ m\left({\tilde{\mathrm{t}}}_1\right)-m\left({\tilde{\upchi}}_1^0\right) $$ mass difference and the decay mode.