1. Whisk together masa harina, flour, baking powder, and salt in a medium bowl. Stir in cheese and corn kernels. Add water, 1/4 cup at a time, stirring after each addition until mixture holds together.

2. Heat 1/4 cup oil in a cast-iron skillet over medium heat until hot but not smoking, about 5 minutes. Meanwhile, scoop a heaping 1/3 cup mixture, and use your hands to shape into a patty, about 1/3 inch thick. Repeat with remaining mixture, forming 8 patties.

3. Working in batches of 4, fry patties, turning once, until golden brown, 2 to 4 minutes per side. Using a slotted spoon, transfer to paper towels to drain. If pan becomes dry, add 2 tablespoons oil for second batch. Cover patties with foil to keep warm, up to 30 minutes.