Nonlinear dynamics of electron-acoustic solitary waves in a magnetized plasma whose constituents are cold magnetized electron fluid, hot electrons featuring Tsallis distribution, and stationary ions are examined. The nonlinear evolution equation (i.e., Zakharov–Kuznetsov (ZK) equation), governing the propagation of EAS waves in such plasma is derived and investigated analytically and numerically, for parameter regimes relevant to the dayside auroral zone. It is revealed that the amplitude, strength and nature of the nonlinear EAS waves are extremely sensitive to the degree of the hot electron nonextensivity. Furthermore, the obtained results are in good agreement with the observations made by the Viking satellite.