Bring a large pot of salted water to a boil. Add the gluten free pasta and cook according to package directions until al dente. Drain and set aside.
In a medium bowl, whisk together the Greek yogurt, mayonnaise, lime juice, chili powder, cumin, smoked paprika, garlic powder, salt, and pepper until smooth.
In a large bowl, combine the cooked pasta, black beans, corn, shredded chicken (if using), and cojita cheese or dairy free feta.
Pour the dressing over the salad and toss to coat evenly.
Chill the salad for at least 30 minutes before serving.
Garnish with additional crumbled cheese, if desired.