We present, for the first time, a set of next-to-next-to-leading order (NNLO) fragmentation functions (FFs) describing the production of charmed-meson D∗ from partons. Exploiting the universality and scaling violations of FFs, we extract the NLO and NNLO FFs through a global fit to all relevant data sets from single-inclusive e+e− annihilation. The uncertainties for the resulting FFs as well as the corresponding observables are estimated using the Hessian approach. We evaluate the quality of the SKM18 FFs determined in this analysis by comparing with the recent results in literature and show how they describe the available data for single-inclusive D*±-meson production in electron-positron annihilation. As a practical application, we apply the extracted FFs to make our theoretical predictions for the scaled-energy distributions of D*±-mesons inclusively produced in top quark decays. We explore the implications of SKM18 for LHC phenomenology and show that our findings of this study can be introduced as a channel to indirect search for top-quark properties.