What is an egg baked in individual serving dish with or without additional ingredients resembles a fried appearance?

The dish you're describing is called a Shirred Egg. It's a culinary preparation in which an egg is baked in a small, individual serving dish, often made of ceramic or porcelain. Additional ingredients such as cheese, vegetables, or meat can be added to enhance the flavor and texture. The dish is typically baked in the oven until the egg is set and cooked through, resulting in a custardy consistency and a slightly browned appearance that resembles a fried egg. Shirred eggs are commonly served for breakfast or brunch, and variations of this dish can be found in different cuisines around the world.