We have recently introduced a new model for the distribution of dark matter (DM) in galaxies based on a self-gravitating system of massive fermions at finite temperatures, the Ruffini–Argü elles–Rueda (RAR) model. We show that this model, for fermion masses in the keV range, explains the DM halo of the Galaxy and predicts the existence of a denser quantum core at the center. We demonstrate here that the introduction of a cutoff in the fermion phase-space distribution, necessary to account for the finite Galaxy size, defines a new solution with a central core which represents an alternative to the black hole (BH) scenario for SgrA*. For a fermion mass in the range mc2=48–345 keV, the DM halo distribution is in agreement with the Milky Way rotation curve data, while harbors a dense quantum core of about 4×106M⊙ within the S2-star pericenter.