We investigate the large-scale fossil magnetic field in the accretion disks of young stars [1,2]. We elaborate an MHD modification of Shakura and Sunyaev’s model [3]. In addition to the equations of Shakura and Sunyaev, we solve the equations of thermal and collisional ionization taking into account main ionization and recombination mechanisms, as well as dust grain evaporation. Induction equation is solved taking into account Ohmic dissipation, magnetic ambipolar diffusion, the Hall effect, and magnetic buoyancy. Analytical solution and numerical simulations of the model equations show that the magnetic buoyancy prevents runaway generation of the toroidal magnetic field, and magnetic field has quasi-azimuthal geometry in the innermost region of the disk. Magnetic field has quasi-poloidal geometry inside the `dead’ zone due to Ohmic dissipation. Ambipolar diffusion operates in the outer part of the disk, and magnetic field is quasi-radial or -azimuthal depending on the ionization rate and recombinations efficiency in this region. The Hall effect influences magnetic field geometry near the boundaries of the `dead’ zone. In the case of classical T Tauri star, magnetic field strength is of 10-300 G near the inner edge of the disk, 0.01 G at typical radial distance r=3 au inside the `dead’ zone, and it approaches interstellar value near the outer edge of the disk. Magnetic plasma beta is not constant over the disk, ranging from 100-1000 at the inner edge to 10^4-^5 inside the `dead’ zone and 1-10 at the outer edge. We compare our results with contemporary observational data on the magnetic field in the protoplanetary disks and show that the model predictions agree with the observations. The work is supported by Russian Science Foundation (project 19-72-10012).