In a medium bowl, whisk together flour, baking powder, salt, paprika, and cayenne; set aside. In a second medium bowl, whisk together eggs and beer. Gradually whisk into dry ingredients to create a batter; transfer to refrigerator to rest for 1 hour.
Heat 2 inches of oil in a large stockpot to 375 degrees. Line a baking sheet with paper towels; set aside. Place one-third of the squid in a medium bowl. Sprinkle with flour, tossing to coat. Add 1/2 cup of batter, and stir to evenly coat. Working quickly, transfer coated rings, one at a time, to hot oil. Fry until cooked through and golden brown, about 1 minute. Transfer to prepared baking sheet to drain. Repeat with remaining squid rings and batter. Serve immediately with lime wedges and salsa.