Can half sibling have a relationship?

Whether or not it is legal depends on what country (or state) you're in, but it would be illegal in virtually all. In most countries/states, it would - legally speaking - be the same as a relationship with a full sibling.

It would, regardless of the law, be strongly discouraged. It would put huge strain on the family, it would be frowned upon and it would disgust most people.

And most importantly: A possible child would be far more likely to have heritable illnesses, and would be at great risk for painful illnesses. Lack of genetic diversity increases the risks of congenital deadly diseases multiple times.