In an answer to the question above, Mark noted, "Legally, a territory is directly governed by the federal government, and can't pick a side. There's no possibility of "withdrawing from the Union" or equivalent." but mentioned that there were certainly Confederate sympathies in many of the existing US territories.
Both during the time of the US Civil War and today, the US Federal Government has claimed jurisdiction over "territories" which (by definition) lack the sovereignty afforded to States. Nowadays, these are mostly offshore islands and archipelagos (e.g. Puerto Rico, the Commonwealth of the Northern Mariana Islands, etc.), but in the 1800's included much of mainland North America (such as New Mexico as mentioned in the linked question).
Did the Confederate States of America (CSA, or Confederacy) ever officially claim jurisdiction over territories outside of the borders of the States that had seceded from the USA? Whether these territories were simultaneously claimed by the USA (as would most likely be the case) doesn't matter. If the CSA passed a law, "For the annexation of the Territory of New Mexico as a territory under the jurisdiction of the Confederate States and the establishment of a legal system for the same guaranteeing the practice of slavery, etc.", that would count even if the CSA was unable to actually exercise any practical "boots on the ground" jurisdiction there.