For the coating and dough: Combine 1/4 cup sugar and 1/2 teaspoon peppermint extract in a resealable plastic bag and rub together until coated; spread on a baking sheet and let dry 1 hour. Mix the peppermint sugar with 3 tablespoons red sanding sugar in a medium bowl. In a separate bowl, whisk 2 eggs, 3/4 cup ricotta, 3 tablespoons sugar and 1/4 teaspoon peppermint extract. Stir in 1 cup self-rising flour.
To fry: Working in batches, deep-fry tablespoonfuls of the dough in 350˚ vegetable oil in a large dutch oven, turning, until golden, about 4 minutes. Remove to a paper towel–lined plate with a slotted spoon and let drain 10 seconds, then toss with the peppermint sugar.