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Abstract Two-particle Azimuthal correlations are measured with the ALICE apparatus in pp collisions at $$\sqrt{s} = 13$$ s = 13 TeV to explore strangeness- and multiplicity-related effects in the fragmentation of jets and the transition regime between bulk and hard production, probed with the condition that a strange meson ( $$\mathrm {K_S}^{0}$$ K S 0 ) or baryon ( $$\Lambda $$ Λ ) with transverse momentum $$p_{\mathrm T} >3$$ p T > 3 GeV/ $$c$$ c is produced. Azimuthal correlations between kaons or $$\Lambda $$ Λ hyperons with other hadrons are presented at midrapidity for a broad range of the trigger ( $$3< p_\mathrm {T}^\mathrm {trigg} < 20$$ 3 < p T trigg < 20 GeV/ $$c$$ c ) and associated particle $$p_{\mathrm T}$$ p T (1 GeV/ $$c$$ c $$< p_\mathrm {T}^\mathrm {assoc} < p_\mathrm {T}^\mathrm {trigg} $$ < p T assoc < p T trigg ), for minimum-bias events and as a function of the event multiplicity. The near- and away-side peak yields are compared for the case of either $$\mathrm {K_S}^{0}$$ K S 0 or $$\Lambda $$ Λ ( $${\overline{\Lambda }}$$ Λ ¯ ) being the trigger particle with that of inclusive hadrons (a sample dominated by pions). In addition, the measurements are compared with predictions from PYTHIA 8 and EPOS LHC event generators.