In a large bowl, combine corn kernels, shredded cheese, cotija cheese, and chopped cilantro.
Add the flour, cornmeal, beaten egg, chili powder, paprika, salt, and pepper. Mix until everything is well combined and holds together when pressed.
Form the mixture into small balls or patties, about 1–2 inches in diameter. Place them on a plate or tray lined with parchment paper.
For Frying: Heat oil in a skillet over medium heat. Fry the bites in batches, turning occasionally, until golden and crispy, about 3–4 minutes per side. Drain on paper towels.
For Baking: Preheat the oven to 400°F (200°C). Arrange the bites on a greased or parchment-lined baking sheet. Spray lightly with cooking spray and bake for 18–20 minutes, flipping halfway through, until golden brown.
Serve warm, topped with sour cream or crema, a sprinkle of cotija cheese, and a squeeze of lime.