Whisk flour, baking powder, salt, and beer in a bowl. Refrigerate batter 1 hour (it will puff while chilling).
Place chiles directly over the flame of gas-stove burners on high heat. Roast, turning with tongs, until skins are charred and blistered. (Alternatively, broil chiles on a baking sheet, turning often, until skin is charred, taking care not to overcook. Otherwise, they will be difficult to peel, and flesh may be too soft to stuff.) When chiles are cool enough to handle, slip skins off.
Leaving stem intact, cut a slit into the side of each chile. Remove seedpod, then insert a stick of cheese.
Heat butter in a skillet over medium heat. Add onion and garlic; saute until onions are translucent, about 5 minutes. Add corn; saute until tender, about 5 minutes. Season with salt and pepper. Spoon 1/4 cup of corn mixture into each chile, and close up with a toothpick.
Heat 1 inch oil in a large nonstick skillet over medium heat until hot. Dip chiles in batter, and fry in batches (do not crowd skillet) until golden, about 1 minute per side. Drain on paper towels. Serve with sour cream and lime wedges.