Measurements of jet fragmentation and jet properties in pp collisions provide a test of perturbative quantum chromodynamics (pQCD) and form a baseline for similar measurements in heavy ion (AA) collisions. In addition, jet measurements in pA collisions are sensitive to cold nuclear matter effects. Recent studies of high-multiplicity final states of small collision systems exhibit signatures of collective effects that could be associated with hot and dense, color-deconfined QCD matter, which is known to be formed in collisions of heavier nuclei. The modification of the jet fragmentation pattern and jet properties is expected in the presence of such QCD matter. Measurements of jet fragmentation patterns and other jet properties in pA collisions are needed in order to establish whether deconfined QCD matter is indeed generated in such small systems. In this contribution, we present measurements of intra-jet properties for leading charged-particle jets in minimum bias p-Pb collisions at $\sqrt{s_{\rm NN}}$ = 5.02 TeV and in minimum bias and high multiplicity pp collisions at $\sqrt{s}$ = 13 TeV. Results are compared with theoretical model predictions.