No, because he already has. A person can only be claimed once.
If your nephew has income of over $4200, he cannot be claimed by anyone else, regardless of the amount of support you provided.
The child is another story. A child can be the “qualifying child” dependent of any close (grand niece counts) relative in the household. Either you or the father can claim the child, but not both. If you can't agree, on who will claim her, then the parent has first choice. There is an additional rule for the situation: the non parent (you) must have a higher income than the parent, to do this.
It may be worthwhile to prepare returns both ways and compare. This tool may be useful: https://turbotax.intuit.com/tax-tools/calculators/taxcaster/?s=1. He can still file an amended return to allow you to claim the child.
