This does not impact your citizenship.
For now, go about your life and if she files for child support or to establish paternity, get thee to a family law attorney. You can have paternity established at that point.
As for support, if one parent has significant assets, then yes, that can be used to help figure CS due. Think actor or athlete who "retired" early so isn't earning a paycheck, or only earning a small amount but has millions in the bank. Your typical savings account with a rainy day fund is "safe".