It's not clear why his dad can't claim him. Usually the parent that the child lives with is the one who can claim the child as a dependent.
Support is not the only thing that determines who can claim a child as a dependent. You probably cannot claim him because he did not live with you for more than half the year. The father is the custodial parent, and your son is probably a "qualifying child" of his father. That means that you cannot claim him, unless you get a signed Form 8332 from the father allowing you to claim the child.
You can use the tool at the following link on the IRS web site to determine whether you can claim your son as a dependent.
Whom May I Claim as a Dependent?
