What are the rights of a child born out of wedlock, and is it permissible to treat them differently from children born within a legitimate marriage?

The child of zina (fornication/adultery) is one whose mother gives birth to him as a result of committing indecency. His lineage is established only through his mother, and he inherits from her. His lineage is not established through the fornicator/adulterer according to the majority of jurists. He is a Muslim if born to a Muslim mother, and he has the rights and obligations of Muslims. It is not permissible to punish him for a crime he did not commit, nor is it permissible to unjustly differentiate between him and legitimate children.