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Heat oil in a dutch oven or deep fryer to 375°F.
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Mix the corn flour and sugar together in a bowl.
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Add the butter, egg, salt, rum and milk, stirring constantly until you have a thick batter.
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Peel the bananas, cut them into quarters, and sprinkle them with a mixture of cinnamon and sugar.
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Roll the banana quarters in the batter and dip them into the hot oil a few at a time.
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Fry them for 2 to 3 minutes on each side, turning once until they are golden brown.
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Drain on absorbent paper and dust with the cinnamon sugar.
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Serve warm.