  This study delves deeply into braneworld scenarios within modified gravity
models, investigating their impact on particle localization and the structure
of branes. Through a comprehensive blend of numerical analyses and theoretical
inquiries, we unravel a nuanced correlation between deviations from standard
General Relativity (GR) and the emergence of split branes. By employing
probabilistic measurements, we pinpoint stable configurations that align with
brane division intervals, thus challenging prevailing assumptions regarding the
gravitational framework of our universe. Furthermore, our investigation extends
to the localization of fermions within the brane, exposing intricate dynamics
shaped by scalar field characteristics and modifications to gravitational
models. By harnessing quantum information measurements, notably Shannon
entropy, we discern heightened probabilities of fermion localization within the
brane as gravitational models diverge from standard paradigms. This underscores
the limitations of General Relativity in comprehensively describing the
complexities inherent in our universe. Lastly, our exploration of massive
fermions unveils their potential to breach the confines of the brane, hinting
at promising avenues for future experimental endeavors aimed at probing the
nature of extra dimensions and gravitational interactions. This suggests
exciting prospects for advancing our understanding of fundamental physics
beyond conventional boundaries.
