Rinse each piece of corn to get rid of all the silk from the cobs or use a corn silker brush. Set aside.
In a small bowl, melt the butter and set aside.
In a separate small bowl, squeeze the juice of the limes and set aside.
Combine the chili powder, smoked paprika, salt, and pepper, mix well. Place in a separate small bowl.
Crumble the cotija cheese and place in a separate bowl.
Using a basting brush, baste the melted butter onto each ear of corn on all sides.
Generously sprinkle each cob with the dry seasoning.
Place each piece on a grill and grill for about 15 minutes or until the kernels start to turn a light brown color. Lightly sprinkle on some cotija cheese and let the corn grill for 2-3 more minutes,
When done, remove the corn from the grill. Take the basting brush and baste on more of the lime juice onto each cob, along with a bit more melted butter.
Top with additional cotija cheese and serve immediately.