This study investigates the interplay between magnetism and superconductivity in the $ t-J $ model of $ La_{3}Ni_{2}O_{7} $ under multiband Gutzwiller approximation. The research focuses on the effects of hole doping on the magnetic and superconducting properties of this nickelate system. The study reveals that the inter-orbital super-exchange process between $ d_{z^{2}} $ and $ d_{x^{2}-y^{2}} $ orbitals leads to complex hole doping dependence in the magnetic properties. The system transitions from a G-AFM state to an A-AFM state with increasing hole doping. The inter-layer superconducting pairing of $ d_{x^{2}-y^{2}} $ orbitals dominates due to the large hopping parameter of $ d_{z^{2}} $ along the vertical inter-layer bonds and significant Hund's coupling between the two orbitals. The G-AFM state and superconductivity can coexist in the low hole doping regime. The study also considers the impact of inter-layer hopping amplitude on the system properties. The results show that the superconducting pairing order is enhanced with increasing inter-layer hopping amplitude. The superfluid stiffness is calculated to distinguish different phases of the system, and it is found that the superconducting dome can extend over a wide doping range. The study concludes that the nickelate $ La_{3}Ni_{2}O_{7} $ is in the strong coupling regime and the system is studied in the large $ J_{H} $ limit. The results suggest that the superconductivity in $ La_{3}Ni_{2}O_{7} $ under pressure may be enhanced by electron doping. The study also highlights the importance of considering the interplay between magnetism and superconductivity in nickelates.This study investigates the interplay between magnetism and superconductivity in the $ t-J $ model of $ La_{3}Ni_{2}O_{7} $ under multiband Gutzwiller approximation. The research focuses on the effects of hole doping on the magnetic and superconducting properties of this nickelate system. The study reveals that the inter-orbital super-exchange process between $ d_{z^{2}} $ and $ d_{x^{2}-y^{2}} $ orbitals leads to complex hole doping dependence in the magnetic properties. The system transitions from a G-AFM state to an A-AFM state with increasing hole doping. The inter-layer superconducting pairing of $ d_{x^{2}-y^{2}} $ orbitals dominates due to the large hopping parameter of $ d_{z^{2}} $ along the vertical inter-layer bonds and significant Hund's coupling between the two orbitals. The G-AFM state and superconductivity can coexist in the low hole doping regime. The study also considers the impact of inter-layer hopping amplitude on the system properties. The results show that the superconducting pairing order is enhanced with increasing inter-layer hopping amplitude. The superfluid stiffness is calculated to distinguish different phases of the system, and it is found that the superconducting dome can extend over a wide doping range. The study concludes that the nickelate $ La_{3}Ni_{2}O_{7} $ is in the strong coupling regime and the system is studied in the large $ J_{H} $ limit. The results suggest that the superconductivity in $ La_{3}Ni_{2}O_{7} $ under pressure may be enhanced by electron doping. The study also highlights the importance of considering the interplay between magnetism and superconductivity in nickelates.