In a medium bowl mix the masarepa, flour, water, milk, salt, sugar and butter. Knead with your hands for about 3 minutes moistening your hands with water as you work.
Form 12 small balls with the dough. Place each ball between 2 plastic bags or parchment paper, and with a flat pot cover, flatten to about ⅛-inch thickness.
Place cheese into the center of half the masa circles and top the with another masa circle of dough. Using your fingers, seal the edges around the arepas, which will prevent the cheese from spilling out.
Add the butter to a nonstick pan over medium heat. Place the arepas in the pan and cook about 3 minutes on each side, until a crust forms or until they are golden brown. Serve immediately.