This study investigates electron dynamics in three distinct discharge modes of a cross-field atmospheric pressure plasma jet: the non-neutral, quasi-neutral, and constricted modes. Using a hybrid Particle-In-Cell/Monte Carlo Collisions simulation, we systematically vary the applied voltage and driving frequency to explore these modes and their transitions. At low power, the discharge operates in a non-neutral mode, characterized by near-extinction behavior, analogous to the chaotic mode in other plasma devices. As power increases, the plasma transitions to a quasi-neutral mode, exhibiting the Ω- and Penning-mode heating mechanisms, similar to the bullet mode in parallel-field jets. At high power, the discharge enters a constricted mode, where plasma density increases significantly, and the discharge contracts toward the electrodes along the entire channel. Experimental validation using phase-resolved optical emission spectroscopy confirms the existence of the constricted mode as a distinct operational regime. These findings provide deeper insights into discharge mode transitions, contributing to the optimization of atmospheric pressure plasmas for various applications.