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I am sorry to hear about this situation. There is no clear appeal if a US Passport is denied, although the US Dept. of State should have a protocol in place to administratively appeal. If the matter is still denied at appeal, one can then send this to court under either a Writ of Mandamus or the APA.
The Writ of Mandamus can be used to compel administrative agencies to act. See 28 U.S.C. § 1361.
The APA is the Administrative Procedures Act, which provides a basis for suit where the government has unreasonably delayed action or fails to act. See 5 U.S.C. §§ 555(b) and 706(l).
You would need an attorney versed in federal and/or administrative law. Let me know if you need help finding someone locally.
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