Preheat oven to 200 degrees F (95 degrees C). Line a baking sheet with paper towels.
Fill a bowl with lightly-salted water. Rinse the grated sweet potato in the water, and drain into a sieve. Pat the grated sweet potato dry with a cloth or paper towels, then place into a bowl. Squeeze excess moisture from the grated onion, and place into the bowl with the sweet potato. Stir the eggs and pepper into the mixture until well combined.
Heat the olive oil in a nonstick skillet over medium heat until it shimmers, and spoon about 1 heaping tablespoon of the potato mixture per patty into the hot oil. Flatten the patties with a fork, and fry until golden brown and crisp on the bottom, 5 to 8 minutes. Flip and cook on the other side, sprinkle with salt, then set the cooked patties aside on the prepared baking sheet in the preheated oven while you finish cooking the latkes. Stir the potato mixture before cooking each batch of patties. Serve hot with applesauce and yogurt.