The spin transport through DNA system formed by a guanine-cytosine is studied extendedly in our work. Hence, theoretical treatment is accomplished for one magnetized active region (includes base pairs and backbone) coupled to ferromagnetic leads in parallel configuration case, throughout magnetic quantum contacts (FM-(G/C)N-FM). Our treatment is based on the tight binding model to derive obvious formula for the spin dependent transmission spectrum which is employed to investigate the spin transport through DNA junction. Our calculations are accomplished in the presence of spin-orbit coupling for strong, weak and "without backbone" regimes. The role the system spin dependent factors of the transport of (G/C)N molecule are investigated in our study. These factors include the molecular length, as well as externally applied bias voltage. Variation of these factors can enhance or suppress spin transport through (G/C)N molecule (with N=10,15,20,25. The transmission spectrum results confirm that the spin transport throughout (G/C)N is originated by a coherent tunneling process between neighboring bases through the overlapping of the LUMO orbitals of the bases. The physical mechanism is raise from quantum interference combination with molecular length and the presence of spin-orbit coupling. The best functional feature for environmental effect, which may induce dephasing such as leads temperature, is investigated. The results showed that the spin-polarized transport can be effectively regulated by the molecular length of (G/C) which can exhibit efficient spin filtering and spin switching