In food processor, pulse ricotta until smooth and creamy. Scrape ricotta into large bowl. In small bowl, lightly beat egg yolks. Beat yolks into the ricotta along with rum and sugar. Sift together flour and baking powder; stir into ricotta mixture.
In clean bowl with clean beaters, beat whites until stiff but not until dry peaks form. Fold gently into ricotta mixture.
In large, heavy-bottomed pan over medium heat, slowly heat at least 4 inches of peanut oil to 350 degees F to 375 degrees F. Before oil reaches smoking point, drop scant tablespoonfuls of batter into hot oil; do not crowd pan. Cook fritters until golden, about 2 minutes per batch (fritters will flip themselves). Remove fritters with slotted spoon to paper toweling to drain. Repeat with remaining batter. Dust with confectioners sugar. Serve immediately. Makes 5 dozen fritters.