<p>The theoretical framework presented herein establishes a direct connection between the radiation temperature function modified by the Extended Generalized Uncertainty Principle (EGUP) and the modified spacetime metric. This enables the construction of an explicit correspondence between the EGUP and metric functions. This research derives the pertinent black hole thermodynamic quantities and calculates the photon sphere radius and black hole shadow size. The results of the study indicate that, in comparison with the Schwarzschild black hole, the event horizon radius remains constant. However, the photon sphere radius increases with the EGUP parameter, while the black hole shadow size decreases, revealing that the EGUP induces an observable optical shift effect. A novel set of constraints on the EGUP parameter is established through a comparison of theoretical predictions with observational data from the Event Horizon Telescope (EHT) for the Galactic center black hole SgrA*. It is noteworthy that when the EGUP parameter approaches a specific value, the originally unstable photon sphere outside the event horizon coincides with a stable photon sphere, forming a critical configuration. The photon sphere at this critical point is termed the extreme photon sphere, and its properties are of significant importance for understanding matter motion in strong gravitational fields as well as the generation and detection of gravitational waves.</p>