Cut fish into strips; set aside. Whisk together eggs and pepper in a shallow dish. In a separate shallow dish, combine the flaxseed, Old Bay Seasoning, salt, breadcrumbs, and Parmesan cheese; blend well.
Coat fish sticks in egg wash, allowing excess to fall off fish; then, dip in bread crumb mixture, coating both sides. Place onto a clean dish until ready to cook. Continue until all fish sticks have been coated.
Heat 1/8 cup of oil in a large skillet over medium-high.
Place half the fish (or less if you are using a smaller skillet) into skillet in a single layer. Cook on each side for 4 minutes, allowing to brown evenly. Set aside and cover to keep warm. Add more oil to the skillet as needed, allowing to reheat before cooking remaining fish sticks.