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Abstract The first measurement of the multiplicity dependence of intra-jet properties of leading charged-particle jets in proton–proton (pp) collisions is reported. The mean charged-particle multiplicity and jet fragmentation distributions are measured in minimum-bias and high-multiplicity pp collisions at center-of-mass energy$$\sqrt{s}$$ $\sqrt{s}$= 13 TeV using the ALICE detector. Jets are reconstructed from charged particles produced in the midrapidity region ($$|\eta | < 0.9$$ $\left|\eta \right|<0.9$) using the sequential recombination anti-$$k_{\textrm{T}}$$ $k_{\text{T}}$algorithm with jet resolution parametersR= 0.2, 0.3, and 0.4 for the transverse momentum ($$p_\textrm{T}$$ $p_{\text{T}}$) interval 5–110 GeV/c. The high-multiplicity events are selected by the forward V0 scintillator detectors. The mean charged-particle multiplicity inside the leading jet cone rises monotonically with increasing jet$$p_\textrm{T}$$ $p_{\text{T}}$in qualitative agreement with previous measurements at lower energies. The distributions of jet fragmentation function variables$$z^{\textrm{ch}}$$ $z^{\text{ch}}$and$$\xi ^{\textrm{ch}}$$ ${\xi }^{\text{ch}}$are measured for different jet-$$p_\textrm{T}$$ $p_{\text{T}}$intervals. Jet-$$p_\textrm{T}$$ $p_{\text{T}}$independent fragmentation of leading jets is observed for wider jets except at high- and low-$$z^{\textrm{ch}}$$ $z^{\text{ch}}$values. The observed “hump-backed plateau” structure in the$$\xi ^{\textrm{ch}}$$ ${\xi }^{\text{ch}}$distribution indicates suppression of low-$$p_\textrm{T}$$ $p_{\text{T}}$particles. In high-multiplicity events, an enhancement of the fragmentation probability of low-$$z^{\textrm{ch}}$$ $z^{\text{ch}}$particles accompanied by a suppression of high-$$z^{\textrm{ch}}$$ $z^{\text{ch}}$particles is observed compared to minimum-bias events. This behavior becomes more prominent for low-$$p_\textrm{T}$$ $p_{\text{T}}$jets with larger jet radius. The results are compared with predictions of QCD-inspired event generators, PYTHIA 8 with Monash 2013 tune and EPOS LHC. It is found that PYTHIA 8 qualitatively reproduces the jet modification in high-multiplicity events except at high jet$$p_\textrm{T}$$ $p_{\text{T}}$. These measurements provide important constraints to models of jet fragmentation.