Heat vegetable oil in a deep pan or skillet over medium-high heat. The oil should be about 2 inches deep.
Carefully add the coated salmon strips to the hot oil, working in batches to avoid overcrowding the pan. Fry for about 3-4 minutes or until golden brown and crispy. Flip the sticks halfway through cooking to ensure even browning.
Once cooked, transfer the fried salmon sticks to a paper towel-lined plate to drain excess oil.
For the Old Bay Blue Cheese Sauce, in a small bowl, combine the crumbled blue cheese, mayonnaise, lemon juice, Old Bay seasoning, and black pepper. Mix well until smooth and creamy.
Serve the Fried Lemon Pepper Salmon Sticks hot with the Old Bay Blue Cheese Sauce on the side for dipping.