No, your child's father can't claim your son simply because he pays child support.

You can allow him to claim the child if you wish, but you'd have to provide him with a signed form 8332: http://www.irs.gov/pub/irs-pdf/f8332.pdf You certainly do not have to give him one, though.

If your father has been providing a home for more than half the year and is providing more than half your son's support, he can claim his grandson.

If your ex does, and your grandfather does, the IRS will flag both returns and ask for proof that the child lives there. Your welfare documents, his school records, medical records will all show that your son lives at the same address as your grandfather. Your ex will have no such proof and will be in a bit of trouble for trying to frivolously claim a dependent.

I can not impress on you enough to get to court and get visitation and child support straight. This will insure you of your rights as far as visitation and name you as the custodial parent. This will also set payments up through probation. Doing this may adjust the amount you get in benefit's but it is important to be assured that you are getting payments correctly when you do go back to work. The process in the court will not happen overnight.

In the mean time. Your father has every legitimate right to claim the child. If and when you get audited the burden of proof will be on your ex. The only way your ex can claim your son is if you allow him to do so.