Heat vegetable oil in a deep-fryer or large saucepan to 375 degrees F (190 degrees C).
Mix the peach preserves, horseradish, and mustard together in a small bowl until well blended; set aside.
Whisk together the flour, baking powder, salt, garlic powder, paprika, cayenne pepper, black pepper, basil, eggs, and beer in a large bowl until smooth.
Add the shrimp in batches to the batter, turning to coat.
Remove with a slotted spoon, shaking off excess batter.
Fry the shrimp in the preheated oil until golden, about 2 minutes.
Transfer the fried shrimp to a paper towel-lined plate to drain.