We reconsider a scenario in which photons and other gauge fields appear as the composite vector bosons made of the fermion pairs that may happen with or without spontaneous violation of Lorentz invariance. The class of composite models for emergent gauge fields is proposed, where these fields are required to be restricted by the nonlinear covariant constraint of type $A_{\mu }{A}^{\mu }=M^2$. Such a constraint may only appear if the corresponding fermion currents in the prototype model, being invariant under some global internal symmetry G, are properly constrained as well. In contrast to the conventional approach, the composite bosons emerged in this way appear naturally massless, the global symmetry G in the model turns into the local symmetry $G_{loc}$, while the vector field constraint reveals itself as the gauge fixing condition. Finally, we consider the case when the constituent fermions generating emergent gauge bosons could be at the same time the preons composing the known quark-lepton species in the Standard Model and Grand Unified Theories.