No. You can only open an FHSA for yourself. And only you, as the FHSA holder, can contribute to your FHSA and claim the deposit as a deduction on your tax return. However, you can gift your child money, which they can deposit in their own FHSA. Income attribution rules generally don't apply to monetary gifts parents give their children to contribute to their FHSA. As a result, you won't have to pay any tax on income or capital gains realized in your child's FHSA account.