Heat oil in a skillet on medium-high heat. Add the diced onions; cook and stir until fluid has evaporated and onions are soft, about 8 minutes.
Stir in hot pepper sauce, sugar, and chili powder. Simmer for about 2 minutes. Add tomato paste and water; stir. Simmer for another 5 minutes. Remove from heat.
Arrange RITZ Crackers on a serving platter and top each cracker with a slice of cooked hot dog. Spoon a small amount of the hot dog onions on top of each.
Drizzle the yellow mustard on top of the onions and serve warm.