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The ALICE Collaboration reports measurements of the large relative transverse momentum ( $k_T$) component of jet substructure in $pp$and Pb-Pb collisions at center-of-mass energy per nucleon pair $\sqrt{s_{\mathrm{NN}}}=5.02\mathrm{TeV}$. Enhancement in the yield of such large- $k_{\mathrm{T}}$emissions in head-on Pb-Pb collisions is predicted to arise from partonic scattering with quasiparticles of the quark-gluon plasma. The analysis utilizes charged-particle jets reconstructed by the anti- $k_{\mathrm{T}}$algorithm with resolution parameter $R=0.2$in the transverse-momentum interval $60<p_{\mathrm{T},\mathrm{ch},\mathrm{jet}}<80\mathrm{GeV}/c$. The soft drop and dynamical grooming algorithms are used to identify high transverse momentum splittings in the jet shower. Comparison of measurements in Pb-Pb and $pp$collisions shows medium-induced narrowing, corresponding to yield suppression of high- $k_T$splittings, in contrast to the expectation of yield enhancement due to quasiparticle scattering. The measurements are compared to theoretical model calculations incorporating jet modification due to jet-medium interactions (“jet quenching”), both with and without quasiparticle scattering effects. These measurements provide new insight into the underlying mechanisms and theoretical modeling of jet quenching.