Place chicken in a large pot and season with fajita seasoning and cayenne pepper. Pour water and beer over chicken. Cook chicken over medium heat until meat falls off the bone and is no longer pink in the center, about 1 hour, adding more water if liquid reduces too much. An instant-read thermometer inserted into the thickest part of the thigh, near the bone should read 165 degrees F (74 degrees C). Transfer chicken from broth mixture to a work surface to cool slightly, reserving broth mixture.
Combine enchilada sauce, jalapeno peppers, onion, and about 1/4 cup chicken broth mixture together in a large saucepan over medium-low heat; cook until onions are softened, about 10 minutes.
Remove meat from chicken and shred into enchilada sauce mixture; mix well.
Warm tortillas on a grill pan over medium-low heat. Spoon chicken mixture into each corn tortilla and top with Mexican cheese blend.