Heat the oil in a skillet on medium-high heat until it reaches a temperature of 325-350 degrees.
Place each cheese stick half onto the center of a wonton wrapper. Wet the tip of your fingers with a little bit of water and moisten the edges of the wonton wrapper so that it will seal nicely. Fold the bottom of the wrapper up over the cheese, followed by both sides, then finally the top to seal. Carefully place the wontons seal side down into the hot oil. Cook until golden brown and crisp, about 1-2 minutes, then flip and cook another 1-2 minutes. Carefully transfer them to a paper towel-lined plate to drain. Serve promptly with warm marinara sauce on the side.