A fake social security number is generally not a obstacle to obtaining an approval of the 601A waiver. If the government can prove that you falsely claimed you were a U.S. Citizen (i.e. on your work records, or voting records) then you will be for ever barred from seeking lawful status in the U.S.
Thus, assuming your 601A waiver is approved, you would depart the U.S. and have an interview at the consulate abroad. If at the interview, you admit that you did claim to be a U.S. Citizen, that admission by you will likely preclude an approval of the visa. What will be the result? You would not be able to lawfully re-enter the U.S. ever. This is a very serious issue, and you should discuss it will an immigration attorney first.
This advise does not create an attorney-client relationship.
Same as in any other circumstances. You said to someone orally or in writing or by action including checking the appropriate box on the forms or engaging in voting on federal state or local level in the USA that you were a USC. Exceptions: children of USCs who might have reasonably believed to be USCs and people who did it erroneously and timely moved to correct the error.
NYC EXPERIENCED IMMIGRATION ATTORNEYS www.myattorneyusa.com; email: firstname.lastname@example.org; Phone: (866) 456-8654; Fax: 212-964-0440; Cell: 212-202-0325. The information contained in this answer is provided for informational purposes only, and should not be construed as legal advice on any subject matter.
False claims of US Citizenship are penalized harshly by the US. There is one very limited exception. I strongly suggest you consult with an immigration attorney so that they may cautiously guide you.
Alvaro De La Calle Calle Law, PLLC (336) 610-5000 www.AsheboroImmigrationAttorney.com www.GreensboroImmigrationAttorney.com