Inclusive J/\u3c8 production is studied in p\u2013Pb interactions at a centre-of-mass energy per nucleon-nucleon collision 1asNN = 8.16 TeV, using the ALICE detector at the CERN LHC. The J/\u3c8 meson is reconstructed, via its decay to a muon pair, in the centre- of-mass rapidity intervals 2.03 < ycms < 3.53 and 124.46 < ycms < 122.96, where positive and negative ycms refer to the p-going and Pb-going direction, respectively. The trans- verse momentum coverage is pT < 20 GeV/c. In this paper, ycms- and pT-differential cross sections for inclusive J/\u3c8 production are presented, and the corresponding nuclear modi- fication factors RpPb are shown. Forward results show a suppression of the J/\u3c8 yield with respect to pp collisions, conc...