Abstract The production of π ± , K ± , and p ¯ p $$ \left(\overline{\textrm{p}}\right)\textrm{p} $$ is measured in pp collisions at s $$ \sqrt{s} $$ = 13 TeV in different topological regions of the events. Particle transverse momentum (p T) spectra are measured in the “toward”, “transverse”, and “away” angular regions defined with respect to the direction of the leading particle in the event. While the toward and away regions contain the fragmentation products of the near-side and away-side jets, respectively, the transverse region is dominated by particles from the Underlying Event (UE). The relative transverse activity classifier, R T = N T/〈N T〉, is used to group events according to their UE activity, where N T is the measured charged-particle multiplicity per event in the transverse region and 〈N T〉 is the mean value over all the analysed events. The first measurements of identified particle p T spectra as a function of R T in the three topological regions are reported. It is found that the yield of high transverse momentum particles relative to the R T-integrated measurement decreases with increasing R T in both the toward and the away regions, indicating that the softer UE dominates particle production as R T increases and validating that R T can be used to control the magnitude of the UE. Conversely, the spectral shapes in the transverse region harden significantly with increasing R T. This hardening follows a mass ordering, being more significant for heavier particles. Finally, it is observed that the p T-differential particle ratios p + p ¯ / π + + π − $$ \left(\textrm{p}+\overline{\textrm{p}}\right)/\left({\uppi}^{+}+{\uppi}^{-}\right) $$ and (K+ + K − )/(π + + π − ) in the low UE limit (R T → 0) approach expectations from Monte Carlo generators such as PYTHIA 8 with Monash 2013 tune and EPOS LHC, where the jet-fragmentation models have been tuned to reproduce e+e − results.