On the basis of the scattering matrix theory and nonequilibrium green function method, we have investigated the fluctuations of charge and spin current of the systems that consist of a quantum dot (QD) with a resonant level coupled to two semiconductor contacts within in alternative site (AS) and alternative bond (AB) framework, where two transverse (B-x) and longitudinal (B-z) magnetic fields are applied to the QD. It is only necessary to use the auto-correlation function to characterize the fluctuations of charge current for a two-terminal system because of the relation that is defined as Sigma S-e(alpha)alpha beta = Sigma S-e(beta)alpha beta = 0. Our that result shows at both auto-shot noise (S-LL) and cross-shot noise (S-LR) are essential to characterize the fluctuations of spin current when Bx is present. Moreover, our model calculations show that the sign of the cross-shot noise of spin current is negative for all surface states of AS/QD/AS junctions, whereas it oscillates between positive and negative values for two surface states of AB/QD/AB junctions as we sweep the gate voltage.