Step 1In a shallow bowl, whisk flour, cornmeal, and Old Bay until well combined. In a food processor, pulse crackers until coarse crumbs form (you can also crush with your hands, or place in a plastic bag and crush with a rolling pin). Transfer crushed crackers to another shallow bowl. Beat eggs to blend in yet another shallow bowl to create a dredging station.
Step 2Working one at a time, coat oyster in flour mixture, tapping off any excess. Coat in egg, then dip into cracker crumbs. Press cracker mixture into oyster to adhere and arrange on a paper towel-lined plate. Repeat with remaining oysters. Refrigerate, uncovered, 10 to 15 minutes.
Step 3In a large pot fitted with a deep-fry or candy thermometer over medium-high heat, heat oil until thermometer registers 375°. Working in batches, fry oysters, letting oil return to temperature between batches, until golden brown and crispy, 1 to 2 minutes, depending on their size.
Step 4Drain oysters on a paper towel-lined plate, then transfer to a platter. Top with chives and serve with lemon wedges alongside.
Step 5Make Ahead: Oysters can be fried 3 days ahead. Transfer to an airtight container and chill.