Can I file for my son that I have to pay support for only part of the year and how much would I get?

Only the custodial parent can claim the child. You can claim if non-custodial parent signs a release Form 8863.
Read: Your U.S. Tax Return: Child of separated or divorced parents (http://taxipay.blogspot.com/2008/03/child-of-separated-or-divorced-parents.html)