Place the potatoes in a cloth, and wring them to remove as much moisture as possible. Mix the potatoes, onion, green onion, eggs, flour, and Cajun seasoning together in a bowl until thoroughly combined.
Heat the oil in a large, heavy skillet over medium heat until it shimmers (oil should be about 1/3 inch deep). Drop about 2 tablespoons of the potato mixture per patty into the hot oil, and flatten the potatoes to make the patties 1/4 to 1/2-inch thick. Brown the patties in the hot oil until golden and crisp on the bottom, about 5 minutes, then flip and cook on the other side. Drain the latkes on paper towels, and serve hot.
