Mix potato, onion, eggs, crackers, salt, and pepper together in a large bowl.
Pour enough vegetable oil into a skillet to fill about 1/2-inch deep; heat over medium-high heat.
Drop spoonfuls of the potato mixture, first pressing potato mixture against the side of the bowl to remove excess liquid, into the hot oil; slightly flatten the latkes into the oil with the back of your spoon so they are evenly thick.
Cook in hot oil until browned and crisp, 3 to 5 minutes per side. Drain latkes on a plate lined with a paper towel.