We investigate the new physics that arises when a correlated quantum impurity hybridizes with Fermi gas with a generalized Rashba spin-orbit coupling produced via a uniform synthetic non-Abelian gauge field. We show that the impurity develops a {it fractional} local moment which couples anti-ferromagnetically to the Rashba-Fermi gas. This results in a concomitant {it Kondo effect with a high temperature scale} that can be tuned by the strength of the Rashba spin-orbit coupling.