In a large bowl, mix the drained canned tuna, chopped onion, grated carrot, green onion, salt, pepper, eggs, and flour. Stir until well incorporated, about 2 minutes.

Take a handful of the mixture and form small patties about 2–3 inches in diameter, aiming for about 8 patties.

Heat oil in a skillet over medium heat until shimmering. Add the patties in a single layer and cook for 2–3 minutes on each side, until golden brown and crisp.

In a separate bowl, whisk together mayonnaise, gochujang, lemon juice, and sugar until smooth and creamy, about 1 minute.

Transfer the cooked patties to a paper towel-lined plate to drain excess oil. Serve warm with spicy mayo.