Put the potatoes in a medium saucepan and cover with water by 1 inch; season with salt. Bring to a boil, then reduce the heat and simmer until tender, about 5 minutes. Drain.
Whisk the sour cream, milk, chives, dill and vinegar in a large bowl. Add the potatoes and cucumber; gently fold to coat. Season with salt and pepper. Set aside.
Mix the flour, 1/2 teaspoon salt and 1/4 teaspoon pepper in a medium bowl. Gently whisk the eggs in another medium bowl. Heat the olive oil in a large nonstick skillet over medium-high heat. Dredge the fish in the flour, shaking off the excess, then dip in the eggs. Add to the skillet and cook until golden and cooked through, about 4 minutes per side. Serve with the potato salad.