Hi, would you mind please reposting your question as a new question? I don't fully understand it. Are you asking if the father is himself receiving child support if he can claim children or if he is paying child support can he claim both children? We also need to know with whom the child is living and if a divorce decree states who can claim the child as a dependent.
In case this helps in the meantime, here is some information from the IRS for non-custodial parents. Paying child support, by itself, does not give a non-custodial parent the right to claim the child as a dependent.
Cheer below if this is helpful.