In a large mixing bowl, combine the ground chicken, chopped onion, shredded zucchini, seasoned bread crumbs, egg, salt, and black pepper until evenly mixed.
Let the mixture rest for about 30 minutes to allow the bread crumbs to absorb moisture and firm up slightly.
Shape the mixture into patties (croquettes) of your desired size and place them on a plate or tray.
Heat the oil in a frying pan over medium to medium-high heat until shimmering.
Cook the patties in the hot pan for about 4 minutes per side, flipping once, until golden brown and cooked through (internal temperature reaches 165°F / 74°C).
Transfer cooked croquettes to a paper towel-lined plate to drain briefly, then serve with a dollop of sour cream and a sprig of fresh dill.