All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Him, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.
The most correct opinion is that [offering] one Udh-hiyah fulfills the obligation for an individual and those among his family he is financially responsible for. The question here implies that the father does not support this son financially. Thus, if it is being asked if the son may be included in the Udh-hiyah his father is offering, it will not be valid for the aforementioned reason. But, if you are asking about a father gifting his son an animal to be slaughtered as Udh-hiyah or paying for it, there will be no harm in that, as it falls under the category of presents.
Allaah Knows best.