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In a large bowl, mix the ground chicken, minced garlic, hot sauce, cream cheese, chopped scallions, and green bell peppers.
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Lay out a few wonton wrappers at a time on a clean work surface.
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Spoon about 1 tablespoon of the chicken mixture onto the center of each wrapper and shredded mozzarella on top.
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Brush the edges of the wrapper with the beaten egg.
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Fold the wrapper over the filling to create a triangle and press the edges together to seal.
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Repeat until all the chicken mixture has been used.
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Heat a few inches of oil in a deep pot or fryer to 350°F.
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Fry the wontons in batches until golden brown, about 2-3 minutes.
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Remove the wontons from the oil with a slotted spoon and drain on a paper towel-lined plate.
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Serve the wontons hot with additional hot sauce for dipping