According to Jain tradition:

• Shwetambar view:

Bhagwan Mahavir married Yashoda and had one daughter, named Priyadarshana (also called Anojja). He did not have any son.

• Digambar view:

Bhagwan Mahavir did not marry at all, so in this tradition he has no wife and no children.

So in both main Jain traditions, there is no son of Mahavir Bhagwan.

You can read more about Mahavir Bhagwan’s family here