If you claim a child as a dependent, that will probably give you a tax credit and increase your refund. So yes it is subject to seizure if you have a debt offset. There is really no way to separate "your part" of your tax return from dependent's "part" of the refund. You are one taxpayer with certain income, deductions and credits and it all goes in the same blender.
However, if your dependent has income and files a tax return, your dependent's tax refund is never taken for your debt; and a child who files a tax return can still be your dependent if they meet the usual requirements.
