In a large mixing bowl, mix the grated sweet potato, leek, half the scallions, half the kimchi, sesame oil, eggs, flour, and salt until smooth.
In a small mixing bowl, add the remaining scallions and kimchi, along with the mayonnaise. Taste for seasoning and add more salt as necessary.
In a large heavy-bottomed skillet (preferably cast iron), heat a thin layer of oil. Add the fritter mixture to the pan in batches, a heaping tablespoon per patty, and fry over medium-high heat until golden on both sides, about 2 minutes per side. Remove the fritters 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). You can keep the early batches warm on a baking sheet in a 400 degree F oven until finished. This can also help get them extra crispy.
Serve immediately with the kimchi aioli and more scallions for garnish.