In the bowl of a food processor, pulse the ricotta until it is smooth and creamy. Turn the ricotta out into a large bowl and add the lightly beaten yolks, the rum, and the sugar, beating well. Sift together the flour and baking powder and add to the ricotta mixture. Add the egg whites to a large bowl and using a whisk or hand-held mixer, beat until stiff but not dry peaks. Fold them gently into the ricotta mixture.
In a large, heavy-bottomed pan over a medium flame, slowly heat at least 4-inches of extra-virgin olive oil. Before the oil reaches the smoking point, form the fritters by dropping scant tablespoonfuls of the batter into the bubbling oil. Cook the fritters until golden, then turn, and cook the other side. Remove with a slotted spoon and drain on paper towels. Repeat with remaining fritter batter.
Dust with confectioners' sugar and serve.