Fragmentation functions, one of the key components of the factorisation theorem used for computing cross sections for heavy-flavour hadron production, are typically constrained in $\textrm e^{+}\textrm e^{-}$ and $\rm e^{-}p$ collisions due to their non-perturbative nature.
However, recent measurements of charm-hadron spectra and ratios at the LHC have questioned the universality of fragmentation functions across leptonic and hadronic collision systems.
This contribution presents measurements of heavy-flavour tagged jets and correlation measurements involving heavy-flavour hadrons. These measurements provide complementary, and more differential, insights on heavy-quark production, fragmentation and hadronization with respect to more inclusive observables.
The studies presented include measurements of the $p_{\rm T}$-differential cross section of D$^{0}$-tagged charm-jets and the longitudinal jet momentum fraction carried by D$^{0}$ mesons and $\rm{\Lambda^{+}_{c}}$ baryons reconstructed inside jets in pp collisions.
The measurements of azimuthal correlations between D mesons and charged particles in pp collisions are presented, to provide a quantitative access to the angular profile, transverse-momentum and multiplicity distributions of the jets produced by the heavy-quark fragmentation. To gain a deeper understanding on possible differences in charm-quark hadronization into mesons or baryons, the comparison of azimuthal correlations between $\Lambda_{c}^{+}$ baryons and D mesons with charged particles in pp collisions is also discussed.