The main aim of this thesis is to use a fermionic dark matter (DM) model (the Ruffini-Arg\"uelles-Rueda (RAR) model) to describe the distribution of dark matter in galactic halos as an astrophysical probe of the fermionic nature of dark matter. My thesis work focuses then on testing possible effects that are caused by DM (and modeled by the RAR model) as well as their astrophysical implications. These effects are also compared with the ones provided by standard density profiles, such as the Navarro-Frenk-White and the pseudo isothermal profiles. My thesis work hence begins the exploration of this broad area by addressing one fundamental question: Is it possible to test and constrain the RAR model (and other DM models) by quantifying its gravitational interaction on some astrophysical systems? I response explicitly to this question, throughout the development of this thesis, presenting viable astrophysical scenarios.