If you file the N-400 stating that you made a false claim to U.S. citizenship and voted in an election there is a high probability that your naturalization application will be denied and you will be put in removal proceedings. There are very few effective defenses to false claims to citizenship charges and no waivers. There may be a possibility of cancellation of removal if you qualify.
YOU MUST SEE A QUALIFIED IMMIGRATION LAWYER BEFORE YOU PROCEED WITH ANY APPLICATIONS TO CIS OR ANY OTHER GOVERNMENT AGENCY THAT YOU MADE A FALSE CLAIM TO U.S. CITIZENSHIP.
That is a major problem.
You really need to retain an experienced immigration lawyer to review all the facts, advise you, and handle the case. You can find one through http://www.ailalawyer.com.
J Charles Ferrari Eng & Nishimura 213.622.2255 The statement above is general in nature and does not constitute legal advice, as not all the facts are known. You should retain an attorney to review all the facts specific to your case in order to receive advise specific to your case. The statement above does not create an attorney/client relationship. Answers on Avvo can only be general ones, as specific answers would require knowledge of all the facts. As such, they may or may not apply to the question.
If you informed the authorities about the error, you may be OK.
NYC EXPERIENCED IMMIGRATION ATTORNEYS www.myattorneyusa.com; email: email@example.com; 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.