Your child is the victim of identity theft, probably by an illegal alien, since they now commit over half of all child-identity theft. Actually, illegal aliens sell SSNs to other illegal aliens, and you can expect far more instances of this. One woman had 57 illegal aliens "working" using her SSN. IRS tried to get her to pay income taxes for ALL 57 of them! That's how she learned her identity/SSN had been stolen.
File reports of identity theft with police, IRS, SSN, FTC. Unlikely they will catch the perpetrator(s) however, especially if it is illegal aliens.
Protect your child's documents! Get child a passport urgently and always keep it up to date. Put passport, original birth certificate, original Social Security card, and everything which can be used to help prove your child is the "real one" in a bank safe deposit box! Get your child a bank account - a trustee account, "Parent Name in trust for Child Name." Deposit regularly. If your child has a well-maintained bank (savings) account, your child can probably convert it to a regular account at age 18. Otherwise, his credit is ruined before he can even open a bank account, get a job, etc.