Single atoms trapped in optical cavities exhibit immense potential as key nodes in future quantum information processing. They have already demonstrated significant advancement in various quantum technologies, particularly regarding the generation of nonclassical light. Here, we efficiently produce genuine photonic Bell states through the inelastic scattering process off single two-level intracavity atoms. An experimental violation of the Bell inequality, arising from the interference between the probability amplitudes of two photons, validates the intrinsic nature of energy-time entanglement. Coupling atoms with an optical cavity in the Purcell regime substantially enhances the two-photon scattering. This Bell state generation process does not require atomic spin control, thereby rendering it inherently immune to decoherence effects. This work advances the comprehension of resonance fluorescence and has the potential to broaden the landscape of quantum technologies and facilitate the application of photonic Bell states.