Take your leftover sweet potatoes out of the fridge. If you have baked ones, scoop the flesh out of the skins and discard the skins. Add it to a large bowl and mash it until it's mostly smooth, with a few small chunks left for texture.
Crack the egg into the bowl with the mashed sweet potato. Stir with a fork until the egg is fully blended in. The mixture should look thick and creamy, almost like a soft dough.
Sprinkle the flour, baking powder, salt, pepper, garlic powder, and smoked paprika over the bowl. Fold everything in gently with a spatula. Stop mixing as soon as the flour disappears, because overmixing makes the fritters dense.
Add the freshly grated cheddar and sliced green onions. Stir just until they are spread evenly through the batter. If the mix feels too sticky to scoop, add one more tablespoon of flour.
Place your skillet over medium heat and add the oil. Let it warm for about two minutes. A tiny drop of batter should sizzle softly when it touches the pan, and that's your sign to start.
Scoop about two tablespoons of batter into the pan for each fritter. Press the top gently with the back of the spoon so it forms a thick round patty. Leave a little space between them so the pan doesn't get crowded.
Cook the fritters for about three minutes until the bottoms are deep golden. Flip them carefully with a spatula and cook another two to three minutes. Cook in batches, adding a little oil to the pan as needed.
Move the cooked fritters onto a plate lined with paper towels. Let them rest for a minute so the oil drains and the crust firms up. Serve them warm while the edges are still crisp.