Step 1 Pour oil to a depth of 2 inches in a large deep skillet; heat over medium-high to 370°F.
While oil heats, whisk together eggs, milk, and hot sauce in a shallow dish; add shrimp to the mixture, and toss to coat.
Whisk together flour, cornmeal, salt, black pepper, and cayenne pepper in a separate shallow dish.
Step 2 Remove 6 to 8 shrimp from egg mixture, shaking excess off; dredge in flour mixture.
Place dredged shrimp in hot oil; fry until coating is golden and crisp, about 2 minutes.
Remove with a slotted spoon to a baking sheet lined with paper towels.
Repeat with remaining shrimp, bringing oil back to 370°F over medium-high heat before adding each batch of shrimp.