There is a factually similar impeachment case. But there might be a court case fitting these facts as well.
No such case is annotated by West under 14th Amendment, Section 3 either with the note or on its list of citations. It is also not mentioned in a law review article looking a WV civil war era jurisprudence up to 1872 when WV's new constitution was adopted.
I suspect that the case you are looking for is a pair of related cases (neither of which involves West Virginia), one tried by the Chief Justice of the U.S. Supreme Court alone on a habeas corpus petition when riding circuit, and a related decision of the Texas Supreme Court involving the same defendant. Griffin's Case, 11 F. Cas. 7, 2 Am. Law T. Rep. U. S. Cts. 93; 8 Am. Law Reg. N. S. 358; 25 Tex. Supp. 623 ; 2 Balt. Law Trans. 433; 3 Am. Law Rev. 784 (Circuit Court, D. Virginia, May 1, 1869) and In re Caesar Griffin, 25 Tex. Supp. 623 (Tex. April 1869).
The official summary of the fact and procedural posture of the main case on point was as follows:
Caesar Griffin, a negro, was indicted in the county court of
Rockbridge county, for an assault with intent to kill. He removed his
case as under the law he had the right to do into the circuit court
for that county, and was there tried by a jury which found him guilty
and assessed his punishment at imprisonment for two years in the
penitentiary. He was accordingly sentenced by the court to that
imprisonment While on his way thither, in the custody of the sheriff
of Rockbridge county, he sent out this writ which was served on the
sheriff. That officer produced the petitioner in the district court
then in session in Richmond, and made return to the writ that he held
him by virtue of the conviction and sentence of the circuit court for
Rockbridge county, making the record of the trial and conviction there
a a part of his return. This return the petitioner traversed, denying
that there was any court or judge in Rockbridge county as pretended by
said pretended record, and that the paper exhibited was any record as
alleged. The state of Virginia appearing by the attorney-general,
Mr., Judge H. W. Sheffey, the judge of the circuit court for
Rockbridge by Bradley T. Johnson, Esq., and the sheriff by James
Neeson, Esq. they joined issue on this traverse. The petitioner then
proved that Judge Sheffey had been a member of the house of delegates
in 1849. That in 1862, he was speaker of the house of delegates, and
that his votes were recorded for affording men, money and supplies to
support Virginia and the Confederate States, in the war then flagrant
with the United States. It was admitted that he was duly appointed on
February 22, 1866, by the then government of Virginia, to be judge of
the circuit including the county of Rockbridge; that he immediately
entered on the duties of that office, and that he has ever since and
still is discharging the functions of the same.
The cause was argued at great length in the district court, before the
district judge in December, 1868, who ordered the discharge of the
petitioner, whereupon an appeal was prayed by the sheriff under the
habeas corpus act of 1867 [14 StaL 385], to the circuit court, and the
petitioner admitted to bail. Before the circuit court could meet other
writs of habeas corpus were sued out by other parties convicted of
felonies, two of them of murder, on the same ground as in this case,
and the petitioners were discharged. A motion was then made by James
Lyons, Esq. in the supreme court of the United States for a writ of
prohibition against the district judge, to restrain him from further
exercise of such power. The supreme court advised on the motion, and
never announced any conclusion, but shortly afterward the chief
justice opened the circuit court at Richmond, and immediately called
up the appeal in Griffin’s Case. This statement is necessary for a
full understanding of the pregnancy of the chief justice’s statement
that the supreme court agreed with him as to the decision he rendered
in this case. In consequence of the failure to oust the state officers
disfranchised under the fourteenth amendment by these and similar
judicial proceedings, congress in February, 1869, passed a joint
resolution directing that all such officers should be removed by the
military commanders of military districts into which the late
Confederate States had been divided. Thus all the old officers of the
state government of Virginia were removed except a very few, and new
ones appointed not obnoxious to the denunciation of the federal bar —
the supreme court of appeals of Virginia; the judges thereof having
been removed by the major general commanding, he appointed as judges
in their stead, a colonel of his staff, and two others, who had held
or did then hold commissions in the United States army. The president
judge of the court performed his functions and drew his pay as colonel
and judge advocate on the staff, overlooking the execution of the laws
of the military, and at the same time those of presiding judicial
officer of the state.
The procedural posture of the case and its result match your description even though the state does not, and there is a supreme court connection even though it is not a U.S. Supreme Court decision.
The West Virginia association is probably a mental mangling of that case with a somewhat similar case from right time frame, a WV murder conviction overturned due to all white jury requirement by U.S. Supreme Court in Strauder v. West Virginia, 100 U.S. 303 (1880).