We discuss the properties of non-Abelian gauge theories formulated on manifolds with compactified dimensions and in the presence of fermionic fields coupled to magnetic backgrounds. We show that different phases may emerge, corresponding to different realizations of center symmetry and translational invariance, depending on the compactification radius and on the magnitude of the magnetic field. Our discussion then focuses on the case of an SU(3) gauge theory in four dimensions with fermions fields in the fundamental representation, for which we provide some exploratory numerical lattice results.