Beat eggs in a mixing bowl. Whisk in milk, then set aside.
Place bread crumbs into a resealable plastic bag; set aside.
Separate and lay an egg roll wrapper onto a flat, clean work surface with one of the tips pointed towards you. Moisten the two far edges of the wrapper with water. Place a string cheese stick onto the corner nearest you, then roll it in 1/3 of the way. Fold over the right and left corners, then continue rolling to the end, pressing to seal. Repeat this step with remaining string cheese sticks and egg roll wrappers.
Heat oil in a deep fryer or large saucepan to 375 degrees F (190 degrees C).
Dip mozzarella sticks into egg mixture, then toss in bread crumbs.
Working in batches, fry breaded mozzarella sticks in hot oil until crisp and golden brown, 3 to 4 minutes.