Combine the flour, sugar, and baking powder in a bowl until thoroughly mixed, and stir in the bananas, vanilla extract, and water to make a smooth, sticky dough.
Heat oil in a deep-fryer or large saucepan to 350 degrees F (175 degrees C). The oil should be deep enough to completely cover the panikekes while frying, or at last 3 inches deep.
Scoop up a scant 1/4 cup of batter with a large spoon, and use another spoon to push it off into the oil. Fry in small batches of 4 or 5 until they float to the top and turn golden brown, about 3 minutes, then flip them to fry the other side. Remove from the fryer and let drain on paper towels.