There are few exceptions. You may fall within one of the few exceptions. However, you do not provide enough information to make a determination.You should have a consultation with an immigration attorney to review your matter.
Mr. Brown is correct, this is super serious ... meet with attorney ... you might have a LIFETIME BAR from the US.
PS I see the significance you are placing on the dates .. something to discuss with the attorney.
PROFESSOR OF IMMIGRATION LAW for over 10 years -- This blog posting is offered for informational purposes only. It does not constitute an attorney-client relationship. Also, keep in mind that this is an INTERNET BLOG. You should not rely on anything you read here to make decisions which impact on your life. Meet with an attorney, via Skype, or in person, to obtain competent personal and professional guidance.
The relevant cut-off date is September 30, 1996. You made your false claim to U.S. citizenship to obtain a benefit under state law after September 30, 1996. Therefore, you are permanently inadmissible to the U.S.
You may have other arguments against the application of this lifetime, unwaivable bar to admission, but the date issue is off the table.
The effective date for IIRIRA was September 30, 1996, not December 29, 1996 as you state. Based upon your facts you made a false claim to U.S. citizenship after the effective date and such a claim makes you permanently inadmissible.
It does appear, however, that you have been in the United States in excess of 10 years and may have a qualifying relative for purposes of applying for cancellation of removal. The false claim issue does not prevent this application for being granted by an Immigration Judge.
Consult with an experienced immigration attorney who can review the facts of your case, advise you as to the options available, and how best to proceed.
While this answer is provided by a Florida Bar Certified Expert in Immigration and Nationality Law, it is for general information purposes only and an attorney/client relationship is neither intended nor created. You should seek out qualified counsel to review your case and provide you with advice specific to your situation. Call +1-561-478-5353 to schedule a consultation with Mr. Devore.