We consider scattering of massless charged Dirac fields propagating in the outer region of de Sitter-Reissner-Nordström Black Holes. The quasinormal frequencies are related to the resonances for semi-classical Schrödinger operators with exponentially decreasing positive potentials. The asymptotic distribution of the resonances are close to the lattice of quasi-poles associated to the non-degenerate maxima of the potentials. Moreover, we describe an expansion of the solution of the evolution equation for the massless Dirac fields in terms of resonances and consider the decay of the solution.