In a deep mixing bowl, stir the flour and sugar together and, with a whisk, beat in the eggs one at a time. Whisking constantly, add the milk, about 1/3 cup at a time and continue to beat until the batter is smooth and elastic enough to stretch like a ribbon from the beater when it is lifted up out of the bowl.
Peel the bananas, chop or slice them coarsely, and drop them into a shallow bowl. With the tines of a table fork, mash the bananas to a smooth puree. Stir the puree into the batter and let the mixture rest at room temperature for about 30 minutes before frying.
Pour oil into a deep fryer or large, heavy saucepan to a depth of 2 to 3 inches and heat the oil until it reaches a temperature of 375 degrees ona deep frying thermometer.
For each fritter, ladle about 1/4 cup of the banana batter into the hot oil. Deep-fry 2 or 3 fritters at a time, leaving enough space between them so that they can spread into 3 or 4-inch rounds or oblongs. Turning them once or twice with a slotted spoon, fry for about 3 minutes or until the fritters are a rich golden color on all sides. as they brown, transfer them to paper towels to drain.
While the fritters are still warm sprinkle them lightly with powdered sugar and serve at once.