In a deep fryer or medium stockpot heat oil or shortening to 400 degrees F. Line a baking sheet with paper towels; set aside.
In a small bowl, combine flour, beer, salt, and pepper. Whisk to combine; set aside.
Stuff each with 1/4-ounce of cheese. Working in batches, dip jalapenos into batter, turning to coat and fry until golden brown 4 to 5 minutes. Transfer to prepared baking sheet to drain. Serve immediately with sour cream.
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