This paper provides a theoretical analysis on the effects of an external Zeeman field and Rashba spin-orbit interactions on superconductivity.We have extensively studied their influence on the superconducting transition temperature Tc and the quasiparticle excitation energy.Our investigation includes a detailed examination of both the s-wave and p-wave pairing states.Implications for the recently discovered family of superconductors,A_2Cr_3As_3(A=Na,K,Rb and Cs),as well as the validation of our theory have been discussed.