No, you cannot deduct an ineligible contribution and would generally be treated as an excess contribution subject to a 6% penalty every year that the excess remains in the account. If the contribution was reported with code W on your W-2, the code W amount must be added to your income. If the excess is corrected before the due date of your tax return, you avoid the 6% penalty and pay tax on any gains on the money while in the HSA account. Correcting the excess after paying one or more 6% excess contribution penalties requires either being able to apply the excess as a subsequent year's contribution or taking a taxable distribution of the excess, subject to a 20% penalty if you are under age 65. The 6% penalty is calculated on the lesser of the excess contribution or your year-end balance in HSAs.
Things are a little different if you were never an HSA-eligible individual. If you were never eligible, the account fails to be an HSA account because only an eligible individual is permitted to establish an HSA account. The account is apparently instead treated as an ordinary investment account, so there would be no excess contribution penalty, but you still need to move the money out to a regular investment account.
