The current PhD research work focuses on the study of the interplay between antiferromagnetism and superconductivity in electron doped cupper based Nd2-xCexCuO4−δ (NCCO) superconductor. Within this system, we have considered the effect of layer coupling, electron doping and annealing, and magnetic field order on superconducting transition temperature (TC). By formulating the system Hamiltonian and by using the retarded double time temperature dependent Green’s function technique, the TC of Nd2−xCe𝑥CuO4 supercponductor is computed quantitatively by considering interlayer interactions as independent variables. Furthermore, we have obtained the mathematical expression for the temperature dependence of superconducting order parameter. The corresponding phase diagrams are also plotted from which we have observed the enhancement of TC for n ≤ 4. Moreover, we have studied the dependence of TC on electron doping, oxygen reduction and magnetic field order in NCCO superconductor by employing the Green’s function technique and Tikhonov regularization method. We have obtained the mathematical expression for the parameters of TC and antiferromagnetic transition temperature (TN) as a function of doping and magnetic field order for NCCO system. By using Tikhonov regularization method, we have determined the quantitative inter-connection of oxygen loses, δ and Ce (x). Furthermore, we have demonstrated that, when an external magnetic field is applied, TC is suppressed whereas TN is enhanced. Moreover, we have calculated the quantitative values of TC as a function of doping and found that, the critical temperature of NCCO occurs in the range of x between 0.05 and 0.27 with TC,max ≈ 25.63 K at x ≈ 0.157, δ~0.02. The electron doping (n type) superconducting phase appears upon suppressing (or degrading) the antiferromagnetic order at about, x = 0.05 − 0.12. This shows the occurance of strong interplay between antiferromagnetism and superconductivity. Furthermore, in this research work, we have investigated the influence of doping, angle and temperature on upper critical magnetic field in layered NCCO superconductor with two band model. By employing the Ginzburg-Landau free energy density functional theory (GL theory), we have calculated the doping and temperature dependence of upper critical magnetic field (HC2), Ginzburg Landau coherence length (ξGL) and Ginzburg Landau penetration depth (ʎGL) based on the configurations of the applied magnetic field parallel to both in plane and out of plane for NCCO superconductor. By using some plausible experimental values for the expression of HC2, ʎGL and ξGL, we have plotted the correspondimg phase diagrams. At optimal doping levels of xopt = 15, xv ||ab ≈ 72.5 T δopt ≈ 0.02, the in plane and out of plane upper critical fields are generated as HC2 and HC2 ||c ≈ 8.05 T respectively. Similarly, for x = 0.12, HC2 of the system becomes, HC2 65.15 T and HC2 ||ab ≈ ||c ≈ 5.05 T which are lower than the values of upper critical magnetic field that are calculated at optimally doping level for NCCO since at optimal doping, antiferromagnetism is suppressed completely resulting in the enhancement of superconducting state so that causes HC2 to be increased. These values are sufficient to suppress the superconductivity because within the under doped regime, an applied magnetic field enhances magnetic order (antiferromagnetism) that could be suppressed by increasing the electron doping reduction annealing. This shows the interplay between magnetism and superconductivity. Moreover, the result shows that the upper critical magnetic field along the ab-plane is greater than the upper critical magnetic field along the out of plane. Our results are in consistence with the previous work. The angle dependent upper critical magnetic fields are also calculated according to their geometry and depict similar trends. Likewise, we have calculated the saturated values of coherence length along the in plane and out of plane to be 𝜁𝐺𝐿 𝑎𝑏~ 6.52 nm and 𝜁𝐺𝐿 𝑐 ~ 0.73 respectively at optimal doping. The theoretical calculations indicate that, the coherence length along the c-axis is less than that of the ab-plane and both decrease as a function of the applied magnetic field. Furthermore, the inter-plane penetration depth, ʎGL ∥c and in plane penetration depth, ʎGL ∥ab are calculated for optimally doped and non-optimally doped Nd2−xCexCuO4−δ superconductor and show significant variations. Similarl to the dome-like shape of the doping dependence of the superconducting transition temperature, both ʎGL ||ab and ʎGL ∥c increase with increasing doping in the under doped regime and become very large near TC at optimal doping ( x ≈15,δ~0.02 ). Finally, we have plotted the phase diagrams for Ginzburg Landau characteristic parameters, K, in plane, KGL ab and inter-plane, KGL c from which the large values indicate that, Nd2−xCexCuO4−δ is a type II superconductor. The results we obtained in this research work are in broad agreement with the experimental findings