A mere falsification of a birth certificate is not a Federal offence, however and Federal use of the same with knowledge of the fraud would be a federal offence. For example, if you use this birth certificate to get Social Security Benefits - then that would be a federal offence.
As Fitzgerald addressed there are a lot of important collateral matters that would need to be considered, such as what your intentions are now to do such a thing as well as going forward what you intend to do, to be able to give a proper answer; as well as understanding family law obligations and other essential components of such a decision.
If this is a course of action you are intent on pursuing I think you would only benefit from retaining an experienced attorney so you can sit down and talk about all of the facts, and the experienced attorney can offer you guidance on all relevant implications under the law.
There is NO attorney-client privilege based on this interaction. I am NOT your attorney. Further, everything we both just wrote is publicly available on the internet and would be the same as if we were talking in a crowded restaurant. If you need legal assistance use Avvo to find a local attorney in your jurisdiction that you feel can best represent your interests as a zealous advocate. My experience is in corporate tax, white collar criminal defense, partnership tax, and tax controversy/litigation. If you're being audited by the IRS or state taxing authority, or you are taking an unusually risky tax position on a return, that is the kind of thing you should have experienced counsel on your side and we can set up an initial consultation. If you have a family law, debt collection, violent crime sort of issue then I do not handle that. Do not contact me for an initial consultation on non-tax matters.
The mere doing of the act would not be fraud. Presentation of the falsified document to obtain something would be.
Not addressed is what difficulties one migh have for falsifying a state document , especially if that denied the true father any benefit.
The above is not intended as legal advice. The response does not constitute the creation of an attorney client relationship as this forum does not provide for a confidential communication.
Whether or not the mere act of putting false information on a birth certificate is an actual federal offense is besides the point. Doing so reflects an intent to deceive, which can haunt you for years to come. It simply is not worth it.