Add the masa, flour, water, beer, and oil to a bowl, stir until a soft dough forms. If the dough is too wet, add additional flour. The consistency should be similar to Play-Doh. Cover the bowl and allow to rest while you prepare the filling.
Heat the oil in a large skillet over medium high heat. Cook the potatoes and bell pepper until softened, about ten minutes. Remove from skillet, set aside.
Add the sausage, cooking until browned, breaking up into small pieces.
Remove from heat, add to the potatoes and red peppers, toss to combine.
Form dough into balls about the size of golf balls.
One at a time place between two sheets of parchment paper (parchment works better than plastic wrap, the dough removes more easily) and using either a tortilla press or a rolling pin, press/roll into 6 inch circles.
Add about 2 tablespoons of filling in the center, top with a pinch of cheddar cheese. Using the parchment, fold over the dough to form a crescent shape. Peel back the parchment and press the dough to seal the edges. Repeat for all dough balls.
Add about 2 inches of the oil in a large skillet over medium high heat until hot.
A few at a time, fry the empanadas until golden brown, turning over halfway through cooking, about 3 minutes on each side.
Allow to drain on a stack of paper towels.