It is sometimes possible to change the date of birth on a naturalization certificate by showing that the mistake was innocent. If you can change the naturalization certificate, then it should be possible to also change the passport. This can only be done by going to court. You should consult with a knowledgeable immigration attorney with litigation experience.
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This might be a very tricky situation. We have had a similar situation in our office where we petition the State Department to change the birthday. Unfortunately it did not work because all the immigration documents reflected a different birthday. You want to make sure that they do not claim you lied on any application, therefore, get a good lawyer to analyze the case before you try to change the birth date.
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