The competition between spin glass (SG) and antiferromagnetic order (AF) is analyzed in two-sublattice fermionic Ising models in the presence of a transverse G and a parallel H magnetic fields. The exchange interaction follows a Gaussian probability distribution with mean À4J 0 =N and standard deviation J ffiffiffiffiffiffiffiffiffiffiffi ffi 32=N p , but only spins in different sublattices can interact. The problem is formulated in a path integral formalism, where the spin operators have been expressed as bilinear combinations of Grassmann fields. The results of two fermionic models are compared. In the first one, the diagonal S z operator has four states, where two eigenvalues vanish (4S model), which are suppressed by a restriction in the two states 2S model. The replica symmetry ansatz and the static approximation have been used to obtain the free energy. The results are showing in phase diagrams T=J (T is the temperature) versus J 0 =J, G=J, and H=J. When G is increased, T f (transition temperature to a non-ergodic phase) reduces and the Neel temperature decreases towards a quantum critical point. The field H always destroys AF; however, within a certain range, it favors the frustration. Therefore, the presence of both fields, G and H, produces effects that are in competition. The critical temperatures are lower for the 4S model and it is less sensitive to the magnetic couplings than the 2S model.