Combine the scallion, sweet potato, kimchi (if using) egg, flour, salt, ground ginger, and cayenne in a large mixing bowl and stir until incorporated.
Heat a thin layer of oil in a large non-stick skillet (preferably cast iron). Add the latke mixture to the pan in batches, a heaping tablespoon per patty, and fry over high heat until dark brown on both sides, about 2 minutes per side. If your stove is uneven, tilt the pan to redistrubte the oil every once in a while. Remove the latkes to a paper-towel lined plate and repeat with the remaining batter, adding more oil as necessary (about 4 batches total, depending on the size of your pan).
Serve immediately with Greek yogurt or sour cream.
To make the latkes in advance, simply reheat on a baking sheet in a 400 degree oven until sizzling, 10 minutes.