In this work we discuss the two-fermions bound state problem in the extreme binding energy limit. To this end, we solve the Bethe-Salpeter equation in Minkowski space for the Yukawa model, where the interaction boson is a vector particle. We use the Nakanishi Integral Representation, which simplify the interaction Kernel of the system. Furthermore, we use the light-front projection which eliminates singularities from the Bethe-Salpeter amplitude. Finally, we obtain an integral equation which we solve numerically.