Whisk together masa harina, flour, baking powder, and salt. Stir in cheese and corn. Stirring constantly, add water, 1/4 cup at a time, just until mixture holds together.
Heat oil in a large cast-iron skillet over medium heat until hot but not smoking. Shape a heaping 1/3 cup corn mixture into a patty about 1/2 inch thick. Repeat, forming 8 patties total. Fry patties in two batches, turning once, until golden brown, 4 to 5 minutes per side; add more oil, if needed, between batches. Using a slotted spatula, transfer to paper towels. Tent cakes with parchment, then foil, to keep warm.