A search for physics beyond the standard model in the final state with two same-flavour leptons (electrons or muons) and two quarks produced in proton-proton collisions at sqrt(s) = 13 TeV is presented. The data were recorded by the CMS experiment at the CERN LHC and correspond to an integrated luminosity of 2.3 inverse femtobarns. The observed data are in good agreement with the standard model background prediction. The results of the measurement are interpreted in the framework of a recently proposed model in which a heavy Majorana neutrino, N(l), stems from a composite-fermion scenario. Exclusion limits are set for the first time on the mass of the heavy composite Majorana neutrino, m[N(l)], and the compositeness scale Lambda. For the case m[N(l)] = Lambda, the existence of N(e) (N(mu)) is excluded for masses up to 4.60 (4.70) TeV at 95% confidence level.