In a large pot, heat the vegetable oil over medium heat. Add the chopped onion and sauté until soft, about 5 minutes. Stir in the minced garlic, cumin, and oregano, cooking for another minute until fragrant.
Add the diced tomatoes with their juice and the chicken broth to the pot. Bring to a simmer and cook for 10 minutes.
Stir in the shredded chicken, corn, black beans, and cilantro. Season with salt and pepper to taste. Simmer for an additional 10 minutes to heat through.
While the soup is simmering, prepare the jalapeño corn fritters. In a mixing bowl, combine the cornmeal, flour, baking powder, salt, and black pepper.
In another bowl, whisk together the buttermilk and egg. Pour the wet ingredients into the dry ingredients and mix until just combined. Fold in the chopped jalapeño.
In a skillet, heat about 1/4 inch of vegetable oil over medium heat. Drop spoonfuls of the fritter batter into the hot oil, cooking until golden brown on each side, about 3-4 minutes per side. Remove and drain on paper towels.
Serve the sopa tarasca hot, garnished with lime wedges and accompanied by the jalapeño corn fritters.