The propagating of electron acoustic solitary waves (EASWs) in relativistically magnetized quantum plasmas which consists inertial cold electrons, inertialess hot electrons and stationary background ions have been theoretically investigated. The modified Zakharov-Kuznetsov (ZK) equation is derived by adopting the standard reductive perturbation method to describe the nonlinear evolution of the EASWs. After discussing the effects of various parameter values on the solitary structures, it is shown that the solitary structures are very sensitive to the relativistic degeneracy effect, the cold to hot electrons number density ratio and the electron exchange correlation effects. The numerical analysis can be well described by the existing analytical theory. Our results may be useful in explaining the physics behind the formation of the EASWs in both astrophysical and laboratory plasmas.