Jet quenching in relativistic heavy ion collisions can have multiple phenomenological consequences: jet energy loss, modification of jet substructure, and induced acoplanarity. In these proceedings, we report a measurement of the jet fragmentation function, which is one of the jet substructure observables, in peripheral Au+Au collisions at $\sqrt{s_{\mathrm{NN}}}=200$ GeV by the STAR experiment at RHIC. In particular, we use a semi-inclusive population of jets recoiling from a high transverse momentum trigger hadron. The fragmentation function is constructed from the fraction of the transverse momentum of charged particles projected onto the jet axis over the transverse momentum of the jet. In a previous STAR publication of the semi-inclusive charged-jet spectra, the Mixed-Event technique was used along with the semi-inclusive approach to remove the uncorrelated background contributions, which enables the measurement of jet distributions at low transverse momentum and large jet radius ($R$) in heavy ion collisions. In this analysis we extend this approach to the measurement of jet fragmentation functions. The reported fragmentation functions are corrected for uncorrelated background and instrumental effects via unfolding. The results are compared to those in PYTHIA simulations for $pp$ collisions.