Preheat your grill to medium-high heat (about 400°F or 200°C).
In a small bowl, combine olive oil, smoked paprika, chili powder, garlic powder, salt, lime juice, and lime zest. Mix well to create a marinade.
Brush each ear of corn generously with the marinade, ensuring they are well-coated.
Place the corn directly on the grill grates and grill for about 10-15 minutes, turning every 2-3 minutes, until the corn is tender and has grill marks.
During the last few minutes of grilling, sprinkle the corn with cotija cheese if using, allowing it to melt slightly.
Remove the corn from the grill and let it cool slightly.
Garnish with additional lime juice, a sprinkle of chili powder, and chopped cilantro before serving.