Put the eggs in a small saucepan and cover with water by 1/2 inch. Bring to a boil over medium-high heat, then remove from the heat, cover and let stand 10 minutes. Remove the eggs with a slotted spoon and transfer to a bowl of ice water to cool, about 5 minutes. Carefully peel the eggs; halve lengthwise and scoop out the yolks into a medium bowl.
Add the mayonnaise, mustard and Old Bay to the yolks and whisk until smooth. Stir in the corn and chives; season with salt. Transfer the mixture to a pastry bag fitted with a large star tip (big enough for the corn kernels to fit through). Pipe into the egg white halves. Refrigerate until ready to serve.
Slice the potatoes into 10 rounds, slightly less than 1/2 inch thick. Heat 1/2 inch vegetable oil in a medium skillet over medium heat until it registers 300 degrees F on a deep-fry thermometer. Fry the potato rounds 4 minutes, then remove with a slotted spoon and drain on paper towels. Increase the oil temperature to 375 degrees F; fry the potatoes again until golden brown and crisp, about 3 more minutes. Drain on clean paper towels and season with salt.
Place a deviled egg on each fried potato round. Top with the crabmeat, some chives and more Old Bay.