Here is a link with some info about Jersey cattle:
http://www.ansi.okstate.edu/breeds/cattle/jersey/index.htm
My grandfather had a registered Jersey dairy during the 1920's - 30's. He had one bull that killed a man. It took 2 men to handle him. He had a ring in his nose. Each man would walk on either side with a stick that had a snap attached to the ring. My husband grew up on a Jersey dairy. My brother-in-law has a Holstein dairy. He does not keep bulls.
I've owned Jersey cows for going on 25 years. My husband breeds our cows AI. We can buy semen and breed our cows from proven quality bulls for less than it costs to keep and maintain a bull for a year. We cut and eat our Jersey bull calves. The meat is tender, fine grained and lean. Dairy cattle meat does not marble.
My husband managed a registered Hereford breeding operation. They had several Jersey spotter bulls. They were scary to work. Talk about a bull that just wanted to fight. Jersey bulls are untrustworthly and dangerous.
That is why you don't see them very often. When the dairies sell their bull calves, people cut them. A Jersey bull at the auction barn will bring way less money per pount than a beef bull.
Your calf is probably a cull. If he were worth keeping entire, you probably would be owning him.
If you plan on using him as a bull, don't make a pet out of him and teach your children to stay out of his pen / pasture. Jerseys reach sexual maturity earlier than beef cattle. Don't be surprised if his attitude changes when his hormones kick in.
What type of cows are you planning on breeding him to?