Your son will always report all his own income on a tax return in his own name. (You can help, of course. But his income does not go on your return.) His SSI may be taxable depending on how much other income he has. It sounds like your son needs to prepare a tax return and see whether he owes or gets a refund. If you are using Turbotax Online, your son will need to make a separate account because each user account can only file one tax return for one person.
