If the Social Security income that he receives is his only income, then he does not have to file a tax return. Assuming that the child is under the age of 19 or under the age of 24 and a full time student then you should be able to claim him as a dependent under the Qualifying Child rules. If you are the custodial parent, then your ex cannot claim him as a dependent unless you release his personal exemption to her by giving her a signed Form 8332.
To be a Qualifying Child -
1. The child must be your son, daughter, stepchild, foster child, brother, sister, half brother, half sister, stepbrother, stepsister, or a descendant of any of them.
2. The child must be (a) under age 19 at the end of the year, (b) under age 24 at the end of the year and a full-time student or (c) any age and permanently and totally disabled.
3. The child must have lived with you for more than half of the year. Temporary absences while away at college are considered living with you.
4. The child must not have provided more than half of his or her own support for the year.
5. If the child meets the rules to be a qualifying child of more than one person, you must be the person entitled to claim the child as a qualifying child.
6. The child must be a U.S. citizen or U.S., Canada or Mexico resident for some portion of the year.
7. The child must be younger than you unless disabled.
