No – it is not recommended. Your dog can eat eggs but fried eggs are not the best option for your dog. The reason being is that fried eggs requires butter or oil and your dog does not need that unnecessary fat in their diet.
A better option for your dog would be a boiled or cooked plain egg.
Eggs that are plain can help settle a dogs upset stomach and are a good source of protein for their diet.
As well eggs have amino and fatty acids that are good for their health. Therefore its best to just feed a plain cooked or boiled egg to your dog instead of a fried egg.