We report a rich anisotropic magnetic phase diagram of Na₃Co₂SbO₆, a previously proposed cobaltate Kitaev candidate, based on field- and temperature-dependent magnetization, specific heat, and magnetocaloric effect studies. At low temperatures, our experiments uncover a low-lying (Formula presented) state with an antiferromagnetic (AFM) ground state and pronounced in-plane versus out-of-plane anisotropy. The experimentally identified magnetic phases are theoretically characterized through classical Monte Carlo simulations within an extended Kitaev-Heisenberg model with additional ring exchange interactions. The resulting phase diagram reveals a variety of exotic field-induced magnetic phases, including double-q, (Formula presented)-AFM, zigzag, and vortex phases.