Falsely impersonating a federal officer or employee of the United States is a federal crime punishable by a fine or up to three years of imprisonment. Anyone who pretends to be someone acting under the authority of any department or agency of the United States, and acts as such, or demands or obtains any money, document, or thing of value by acting as such, is guilty of False Personation.

To be guilty of falsely impersonating a federal officer, the offender must knowingly undertake a false identity or persona of a federal official. The pretended character must assert or appear to act under the authority of the United States, such that the false pretense causes the person deceived to rely on the asserted authority. The pretended identity does not have to be one from an existing federal department or agency. For example, pretending to be a federal bookseller of presidential documents—an office that does not officially exist—has been held to satisfy the statute. Having assumed a false federal identity, the offender must then also undertake an overt act under the authority of the false persona. In this way, the statute requires both a state of mind of adopting a false pretense and an overt act consistent with the assumed identity.

https://www.hg.org/legal-articles/falsely-impersonating-a-federal-officer-what-is-the-penalty-53754

(1) impersonates a public servant with intent to induce another to submit to the person's pretended official authority or to rely on the person's pretended official acts;  or

(2) knowingly purports to exercise, without legal authority, any function of a public servant or of a public office, including that of a judge and court.

(b) An offense under this section is a felony of the third degree