Combine mayonnaise, garlic, and the juice of 1/4 lime in small bowl. Mix until well combined, set to the side. Spread cheese on a plate and set aside.
Brush grill grate with vegetable oil and heat grill to high. Grill corn. Turn occasionally until cooked and lightly charred, about 10 minutes.
Immediately brush the corn with butter, if using, then the mayonnaise. Roll corn in cotija cheese. Sprinkle with chili powder, salt, and cilantro. Squeeze lime over corn and serve immediately, with more lime wedges.