The S-stars motion around the Galactic center implies that the central gravitational potential is dominated by a compact source, Sagittarius A* (Sgr A*), with a mass of about 4 × 10 6 M , traditionally assumed to be a massive black hole (BH). Particularly important for this hypothesis, and for any alternative model, is the explanation of the multiyear, accurate astrometric data of the S2 star around Sgr A*, including the relativistic redshift which has been recently verified. Another relevant object is G2, whose most recent observational data challenge the massive BH scenario: its post-pericenter radial velocity is lower than the expectation from a Keplerian orbit around the putative massive BH. This scenario has traditionally been reconciled by introducing a drag force on G2 by an accretion flow. Alternatively to the central BH scenario, we here demonstrate that the observed motion of both S2 and G2 is explained in terms of the dense core -diluted halo fermionic dark matter (DM) profile, obtained from the fully relativistic Ruffini-Argüelles-Rueda (RAR) model. It has been already shown that for fermion masses 48 -345 keV, the RAR-DM profile accurately fits the rotation curves of the Milky Way halo. We here show that the solely gravitational potential of such a DM profile, for a fermion mass of 56 keV, explains: 1) all the available time-dependent data of the position (orbit) and line-of-sight radial velocity (redshift function z) of S2; 2) the combination of the special and general relativistic redshift measured for S2; 3) the currently available data on the orbit and z of G2; and 4) its post-pericenter passage deceleration without introducing a drag force. For both objects, we find that the RAR model fits better the data than the BH scenario: the mean of reduced chi-squares of the time-dependent orbit and z data are, for S2, χ2 S2,RAR ≈ 3.1 and χ2 S2,BH ≈ 3.3 and, for G2, χ2 G2,RAR ≈ 20 and χ2 G2,BH ≈ 41. If we look at the fit of the corresponding z data, while for S2 we find comparable fits, i.e, χ2 z,RAR ≈ 1.28 and χ2 z,BH ≈ 1.04, for G2 only the RAR model can produce an excellent fit of the data, i.e. χ2 z,RAR ≈ 1.0 and χ2 z,BH ≈ 26. In addition, the critical mass for gravitational collapse of a degenerate 56 keV-fermion DM core into a BH is ∼ 10 8 M . This result may provide the initial seed for the formation of the observed central supermassive BH in active galaxies, such as M87.