Heat a large skillet over medium heat.
Add the shredded cooked chicken to the skillet and sprinkle with chili powder, cumin, garlic powder, onion powder, smoked paprika, dried oregano, salt, and cayenne pepper; stir to coat the chicken evenly with the spices.
Stir in the diced tomatoes (with their juices), tomato paste, chopped green chiles, and 1/4 cup water or chicken broth; combine until the tomato paste is evenly distributed.
Cook, stirring occasionally, for about 5 minutes or until the mixture is heated through and flavors are combined; add a little more water or broth if the chicken seems dry.
Taste and adjust seasoning with additional salt, cayenne, or hot sauce if desired.
Use the Mexican shredded chicken immediately in tacos, burritos, enchiladas, salads, nachos, burrito bowls, or other favorite dishes.