Hmmm, not a lawfag so hopefully one can chime in.
The US Virgin Islands are an unincorporated organized territory and an Article IV court. Appeals of the court's decisions are taken to the United States Court of Appeals for the Third Circuit in Philadelphia.
The current judges were appointed by BO, GWB, WJC. See attached.
https://en.wikipedia.org/wiki/District_Court_of_the_Virgin_Islands
Article IV tribunals
Article IV tribunals are the United States territorial courts, established in territories of the United States by the United States Congress, pursuant to its power under Article Four of the United States Constitution, the Territorial Clause.[3] Many United States territorial courts are defunct because the territories under their jurisdictions have become states or have been retroceded.
An example of a territorial court is the High Court of American Samoa, a court established pursuant to the Constitution of American Samoa. As an unincorporated territory, the Ratification Act of 1929 vested all civil, judicial and military powers in the President, who in turn delegated authority to the Secretary of the Interior in Executive Order 10264, who in turn promulgated the Constitution of American Samoa, which authorizes the court. As such, the Secretary retains ultimate authority over the courts.[4]
Other United States territorial courts still in existence are:
District Court for the Northern Mariana Islands
District Court of Guam
District Court of the Virgin Islands