Start by preparing the cherry filling. In a small saucepan, combine the cherries, sugar, cornstarch, water, and vanilla extract. Cook over medium heat, stirring constantly, until the mixture thickens and becomes syrupy, about 5-7 minutes. Remove from heat and set aside to cool.

Prepare the cheesecake filling by beating the softened cream cheese, sugar, and vanilla extract in a bowl until smooth. Add the egg, sour cream, and flour, mixing until fully combined and creamy.

Spoon about 2 tablespoons of the cheesecake mixture into small, round balls (about 1 to 1.5 inches in diameter). Place a spoonful of the cherry filling in the center of each ball and seal the edges tightly, forming a round shape.

For the batter, whisk together the flour, cornstarch, baking powder, sugar, and salt in a bowl. Add the egg, milk, and vanilla extract, and stir until a smooth batter forms.

Heat the vegetable oil in a deep fryer or large, deep pan to 350°F (175°C). Dip each cheesecake ball into the batter, coating it completely, and carefully lower it into the hot oil.

Fry the cheesecake balls in batches for about 2-3 minutes, or until golden brown and crispy. Use a slotted spoon to remove the balls from the oil and place them on paper towels to drain excess oil.

Once all the balls are fried, dust them with powdered sugar and garnish with additional cherries, if desired.

Serve immediately while still warm for a crispy and creamy experience.