It's not clear why you would owe an additional $68 unless something was changed on the tax return. The social security number (SSN) would not create a change in tax owed or refund.
You should attach a copy of the return you already filed with IRS to a letter and a copy of your social security card from the Social Security Administration (SSA) as proof of your correct number. Write "Duplicate" on the top of the tax return copy you send with the letter. The letter should explain that you accidentally entered the wrong SSN on the original return that was file.
This will allow the IRS to correct your SSN and attach your tax return to the correct SSN. An amendment is not required in this situation because you are changing personal information not income, deductions, credits or payments.
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to File Paper Returns With or Without a Payment