There were no confederate district federal courts, at least no records exist of any decision being handed down by one. There was no confederate supreme court, no confederate judiciary at all other than individual state courts. I'm not aware of any confederate version of the U.S. Marshal. Absent a federal court system what purpose would they have served?
Then how do you explain the following from the November 24, 1864, Daily Picayune?
Our readers have seen the anouncement of the sentence of A. W. McKee by a court-marshal in Louisiana, to be shot, and of the decision by Judge Moise, of the Confederate States District Court in Louisiana, that the court marshal had no jurisdiction over McKee [a civilian], and releasing him from their bonds, to answer any civil offense for which he might be prosecuted.
You seem fond of making claims that others would have a hard time disproving. In this case, however, Gotcha!
This supposedly nonexistent 1864 Confederate States District Court seems to have anticipated the 1866 US Supreme Court ruling in ex parte Milligan. Pity the Yankees didn't have courts willing to stand up in wartime for their citizens' rights (Taney's ex parte Merryman ruling excepted).
The United States National Archives and Records Administration disagrees with you. They have the records of these courts in the National Archives (Record Group 21). See below:
21.2.6 Records of the Confederate States District Court for the Middle Division of the District of Alabama
21.2.9 Records of the Confederate States District Court for the Southern Division of the District of Alabama
21.11.3 Records of the Confederate States District Court for the Northern District of Florida
21.12.4 Records of the Confederate States District Court for the Northern Division of the District of Georgia
21.12.9 Records of the Confederate States District Court for the Southern Division of the District of Georgia
21.20.5 Records of the Confederate States District Court for the District of Louisiana
21.26.2 Records of the Confederate States District Court for the Northern Division of the District of Mississippi
21.35.6 Records of the Confederate States District Court for the District of North Carolina
21.45.5 Records of the Confederate States District Court for the Middle Division of the District of Tennessee
21.46.7 Records of the Confederate States District Court for the Southern District of Texas
21.46.10 Records of the Confederate States District Court for the Western District of Texas
21.49.6 Records of the Confederate States District Court for the Western District of Virginia
I may have missed some, but the point is made. I hope the source is acceptable to you...