1. Make the filling: Combine first four ingredients in a medium bowl and season with salt. Gently fold to combine, and set aside. (Crab mixture can be made up to 4 hours ahead—cover and keep in refrigerator until ready to fry.)
2. Make the batter: In a large saucepan fitted with a deep-fry thermometer, pour oil to a depth of 6 inches. Heat over medium-high heat until thermometer registers 375 degrees. While oil is heating, whisk together flour, cornstarch, baking powder, and salt in a large bowl. Gradually whisk in beer until just blended (the batter will be thick).
3. Working in batches of about four beignets at a time, and returning oil to 375 degrees between batches, measure 1 heaping tablespoon crab mixture, roll into a ball, and drop into batter. Using a fork, toss to coat and lift from batter, letting excess drip back into bowl. Carefully lower beignet into oil. Fry, turning occasionally, until crisp and deep golden brown, about 4 minutes. Transfer to a paper towel-lined plate and season with salt.
From Two Ways to Beignet.