Mix cream cheese, Monterey Jack cheese, jalapeño peppers, green onions, and garlic in a medium bowl.
Fill wonton wrappers with approximately 1 teaspoon of cream cheese mixture each. Fold wrappers into triangles and press the edges with a moistened fork to seal.
Heat oil over medium-high heat in a large, deep skillet. Drop 4 wontons at a time into the oil and quickly fry, turning once. Remove when golden brown and drain on paper towels.
