This work investigates the localized control of magnetization reversal in square artificial spin ice (SASI) systems through the introduction of vertical control elements (VCEs). This research focuses on the effects of localized magnetic fields created by VCEs on the magnetization dynamics within SASI. We explore theoretical considerations and implementation strategies for using VCEs to modulate the energy barriers of individual spin flips, thereby influencing the overall magnetization reversal process. Using a single-spin flip Monte Carlo algorithm, we simulate the hysteresis behaviour of a 16-spin SASI system with and without the presence of VCEs. The simulation parameters are chosen to include thermal fluctuations at low temperature and field symmetry breaking. The results demonstrate that VCEs can effectively pin or facilitate the flipping of specific spins, allowing for controlled domain wall nucleation and propagation, mediated by motion of the lattice excitations, known as monopole charges. This control over monopole charge dynamics has potential applications in magnetic storage devices and spintronic technologies. The study provides insights into the impact of the controlled application of localized magnetic fields on the energy landscape of ASI systems.