Put the cooking oil into a large sauté pan. It should be at least 3/4-inch deep; add more oil if needed. Set heat to medium.
While the oil heats, place the flour, beaten eggs, and bread crumbs into separate bowls. Mix a large pinch each of salt and pepper into the flour and into the bread crumbs. One by one, dredge the fish strips in the flour, the egg, and then the bread crumbs, pressing them in to coat evenly. Place the breaded strips on a baking sheet tray.
Drop some bread crumbs into the oil. If they sizzle and float right away, the oil is ready; if they immediately sink, the oil still needs to heat up further. When the oil is ready, carefully place the breaded fish strips into the oil in an even layer but not touching. Let them cook undisturbed for 2-3 minutes per side or until golden-brown. If they brown too quickly, set the pan off of the heat for a bit to allow the oil to cool and lower the stove heat slightly.
When the fish sticks are cooked, immediately remove them from the sauté pan onto a paper towel-lined plate or tray. Let them cool for a few minutes before serving, and serve with the dipping sauce.
While the fish sticks cook, make the dipping sauce by mixing together the sour cream, mayo, and Anytime Sauce into a small bowl to combine. Season to taste with salt, pepper, and more sauce if needed.