Abstract: The synthesis of heavy elements beyond the iron peak remains a partially unresolved problem in nuclear astrophysics. About 99% of these heavy nuclei are produced via the slow and rapid neutron-capture processes. A small fraction of neutron-deficient isotopes are bypassed by them. These approximately 35 proton-rich nuclei, ranging in mass from Se to Hg, are known as the p-nuclei. Based on current models, the majority of p-nuclei is synthesized via photodisintegration reactions in the so-called γ-process (rapid neutron-capture process), which occurs within the O/Ne-rich burning shells of core-collapse supernovae. The passage of the shock front through these layers induces a transient heating to temperatures between 2.0 and 3.5 GK, allowing the partial photodisintegration of pre-existing seed nuclei. In any case, network calculations are essential for reproducing p-nuclei abundances, requiring a network including nearly 20 000 nuclear reactions of almost 2 000 nuclei in the Ni-Bi region. The γ-process relies heavily on the Hauser-Feshbach (HF) statistical model and the various nuclear ingredients in such a framework. In reality, it remains a challenge to validate the reliability of the HF model and its inputs, and accordingly to put the γ-process calculations on a more reliable base. Therefore, it is imperative to constrain the HF models using the experimental data. Despite the success of the γ-process in explaining most p-nuclei, the origin of the ¹³⁸La remains a key unresolved question in nucleosynthesis. ¹³⁸La is underproduced in all γ-process calculations performed so far. The low abundance of ¹³⁸La has prompted the investigation of non-thermonuclear process. Although the νₑ capture on ¹³⁸Ba has been shown to be the most efficient mechanism for producing solar ¹³⁸La, a substantial thermonuclear origin cannot be excluded. This would require that the protosolar nebula was enriched in p-nuclei by sources other than typeⅡsupernovae. In particular, sub-Chandrasekhar mass white dwarf explosions are considered potential significant contributors. The thermonuclear origin of ¹³⁸La critically depends on the competition between its production via ¹³⁹La(γ, n) and its destruction via ¹³⁸La(n, γ). To investigate the contribution of the γ-process to ¹³⁸La production, a comprehensive illustration of constraining the HF theoretical models was presented using the ¹³⁹La(γ, n)¹³⁸La experimental data, and the most influential nuclear models were identified. The optimized models can be employed to evaluate the plasma reaction rates of the ¹³⁹La(γ, n)¹³⁸La. The extracted reaction rates of ¹³⁹La(γ, n)¹³⁸La were also compared with those from the JINA reaction library. Our recommended rate is more than a factor of two higher than that in the JINA at 2.5 GK. Such a discrepancy has the potential to partially mitigate the underproduction of ¹³⁸La.