[en] Heavy quarks (charm and beauty) are essential probes of the quark-gluon plasma (QGP), a hot and dense medium created in heavy-ion collisions. Since the heavy-quark production in high-energy collisions occurs earlier than the formation time of the QGP, heavy quarks witness the whole evolution of the QGP. Measurements in proton-nucleus (pA) collisions provide the genuine testing ground to study possible modifications of heavy-quark production in the presence of a nucleus, which is necessary information to interpret the measurements in heavy-ion collisions. A valuable observable is the production of J/ψ mesons, a bound state of a $c\stackrel{¯<!--\; ??\; -->}{c}$ pair. Their production can be prompt, meaning that they are either produced directly or from the decay of heavier charmonium states, or it can be nonprompt when originating from the decay of beauty hadrons. Therefore, a measurement of J/ψ which separates these contributions allows one to study charm and beauty quark production simultaneously. In this thesis work, the J/ψ meson production was measured in p-Pb collisions at $\sqrt{s_{NN}}$ = 8.16 TeV using a high-p${}_T$ electron enriched data sample collected using the Transition Radiation Detector (TRD). Based on the electron identification and tracking capabilities of the ALICE detector at the LHC, the J/ψ mesons are reconstructed in the dielectron decay channel at midrapidity. Relying on the long lifetime of beauty hadrons, prompt and non-prompt J/ψ contributions are separated on a statistical basis. The resulting p${}_T$ dependent nuclear modification factors (R${}_{pA}$) of prompt and non-prompt J/ψ are consistent with unity within measured uncertainties at midrapidty in 2 < p${}_T$< 14 GeV/c. Further, the results are described by theoretical calculations that include cold-nuclear-matter effects in p-Pb collisions. Thus, the result suggests a small impact of cold-nuclear-matter effects for charm and beauty quarks in the measured kinematic region.