The inclusion of hafnium (Hf) at cerium (Ce) site to form the (Ce1-ₓHfₓO2) lattice system at a concentration content of x = 0.25 would have impact on enhancing the physical properties of the simulated configuration. DFT was used to perform the calculations supported by the Hubbard factor (U). The generalized gradient approximation (GGA-PBE) was employed to analyze the electronic, structural, optical, and mechanical properties at pressures (P = 0, 25, 50, 75, and 100 GPa). The ground state geometry of the pristine fluorite CeO2 corresponds to 5.438 Å, signifying an excellent agreement with the available published literature. The calculated lattice parameter of Ce0.75Hf0.25O2 is diminished to 5.327 Å . CeO2 exhibits a semiconductor character with a direct band gap of 3.134 eV while the band gap of the Ce0.75Hf0.25O2 system was reported to be 3.073 eV, demonstrating slight degradation. However, under pressures, the results demonstrate a gradual increment in the band gap energy of Ce0.75Hf0.25O2 until reaching 3.861 eV at 100 GPa. Furthermore, the thermodynamic feasibility was investigated via chemical potential approach. The pressure-dependent optical properties were extensively discussed of Ce0.75Hf0.25O2, demonstrating enhancing optical properties in the ultraviolet (UV) region motivating its suitable utility for microelectronics.