Final answer:
The cellular process most affected in a genetic disease resulting from a mutation in the AIRE gene is negative selection of self-reactive thymocytes, leading to polyglandular autoimmune syndrome Type-1.
Step-by-step explanation:
In a genetic disease resulting from a mutation in the AIRE gene, the most affected cellular process leading to autoimmunity is negative selection of self-reactive thymocytes. This process ensures that potentially harmful T cells are eliminated in the thymus during development. The specific disease associated with this gene defect is polyglandular autoimmune syndrome Type-1, which is characterized by autoimmunity targeting multiple endocrine organs.