Do miniature cows exist which can be taken as a pet in home? Ideally they should be genetically improvised to have the agility and enthusiasm of a cat. It may sound impossible but I imagine it to be realistic,So does such a miniature pet cow exist or can it be bred?
Miniature cows do exist, they were bred to fit smaller acreage farms. They typically grow to be about 3-4 feet tall (measured from the ground to their shoulder I believe). They're usually kept as pets, or for milk - Due to their small stature there's not much use to keep them for their meat.
I honestly have no idea what you expect with "cat-like agility". No matter what size it is, it's still going to be a cow. The muscles and skeletal structure is exactly the same as a normal sized cow. In order to make the animal I think you're imagining, you would have to make it yourself. Which isn't something we'll be doing anytime soon. Really, if it sounds impossible, it is. Otherwise you'd be hearing about it in the news.