Babruvahan was son of Arjun and Chitrangada. But his story has different versions from different places i read. In some, Ulupi trained him to kill Arjun to later revive him.
What was this story according to original Mahabharat?
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The story of Babruvahan defeating Arjuna starts from here
Vaisampayana said, 'The ruler of Manipura, Vabhruvahana, hearing that his sire Arjuna had arrived within his dominions, went out with humility, with a number of Brahmanas and some treasure in his van. 2 Remembering, however, the duties of Kshatriyas, Dhananjaya of great intelligence, seeing the ruler of Manipura arrive in that guise, did not approve of it.
and ends here.
The chief of the deities himself is incapable of vanquishing thee in battle. The son is one's own self. It is for this that thou hast been vanquished by him.