This study presents a groundbreaking investigation into the profound impact of Hall current on Wave propagation in advanced thermo-diffusive semiconducting materials. By harnessing a higher- order fractional heat equation and incorporating external magnetic fields, our research unveils the intricate dynamics governing wave behavior in these complex systems. The finding sreveal significant alterations in wave speeds, amplitude ratios, and energy distribution, underscoring the critical role of Hall current in shaping thematerial's response. Furthermore, our analysis of reflected waves at the solid'sfree surface demonstrates the pivotal influence of Hall current on wavereflection characteristics. The incident longitudinal P-wave is shown to besignificantly affected, with notable variations in amplitude ratios and phaseshifts. These results have profound implications for understanding wave-matter interactions and optimizing material performance in various applications. This pioneering work offers profound insights into the underlying physics, with far reaching implications for diverse fields, including mechanics, geophysics, and materials science.