The p T-differential production cross sections of prompt and non-prompt (produced in beauty-hadron decays) D mesons were measured by the ALICE experiment at midrapidity (| y | < 0.5) in proton-proton collisions at $\sqrt{s}$ $$ \sqrt{s} $$ = 5.02 TeV. The data sample used in the analysis corresponds to an integrated luminosity of (19.3 ± 0.4) nb −1. D mesons were reconstructed from their decays D0 → K − π+, D+ → K − π+π+, and $D_s^{+}\to \varphi {\pi }^{+}\to K^{-}{K}^{+}{\pi }^{+}$ $$ {\mathrm{D}}_{\mathrm{s}}^{+}\to \upphi {\uppi}^{+}\to {\mathrm{K}}^{-}{\mathrm{K}}^{+}{\uppi}^{+} $$ and their charge conjugates. Compared to previous measurements in the same rapidity region, the cross sections of prompt D+ and $D_s^{+}$ $$ {\mathrm{D}}_{\mathrm{s}}^{+} $$ mesons have an extended p T coverage and total uncertainties reduced by a factor ranging from 1.05 to 1.6, depending on p T, allowing for a more precise determination of their p T-integrated cross sections. The results are well described by perturbative QCD calculations. The fragmentation fraction of heavy quarks to strange mesons divided by the one to non-strange mesons, f s /(f u + f d), is compatible for charm and beauty quarks and with previous measurements at different centre-of-mass energies and collision systems. The $b\overline{b}$ $$ \mathrm{b}\overline{\mathrm{b}} $$ production cross section per rapidity unit at midrapidity, estimated from non-prompt D-meson measurements, is $d{\sigma }_{b\overline{b}}/dy\left({}_{\left(y\right)<0.5}=34.5\pm 2.4{\left(\text{stat}\right)}_{-2.9}^{+4.7}\left(\mathrm{tot}.\text{syst}\right)\right)$ $$ \mathrm{d}{\sigma}_{\mathrm{b}\overline{\mathrm{b}}}/\mathrm{d}y\left|{}_{\left|\mathrm{y}\right|<0.5}=34.5\pm 2.4{\left(\mathrm{stat}\right)}_{-2.9}^{+4.7}\left(\mathrm{tot}.\mathrm{syst}\right)\right. $$ μb. It is compatible with previous measurements at the same centre-of-mass energy and with the cross section pre- dicted by perturbative QCD calculations.