A detailed and general study of the fermionic structure of the 331 models with $\ensuremath{\beta}$ arbitrary is carried out based on the criterion of cancellation of anomalies. We consider models with an arbitrary number of lepton and quark generations, but which require associating only one lepton and one quark $SU(3{)}_{L}$ multiplet for each generation, and at most one right-handed singlet per each left-handed fermion. We see that the number of quark left-handed multiplets must be 3 times the number of leptonic left-handed multiplets. Furthermore, we consider a model with four families and $\ensuremath{\beta}=\ensuremath{-}1/\sqrt{3}$ where the additional family corresponds to a mirror fermion of the third generation of the standard model. We also show how to generate ansatz about the mass matrices of the fermions according to the phenomenology. In particular, it is possible to get a natural fit for the neutrino hierarchical masses and mixing angles. Moreover, by means of the mixing between the third quark family and its mirror fermion, a possible solution for the ${A}_{\mathrm{FB}}^{b}$ discrepancy is obtained.