How did New Mexico's civilians support the effort?

c keeping prisoners of war in their prisons.

Explanation:

The Santa Fe Expedition was an attempt to claim parts of Northern New Mexico for the Republic of Texas in 1841. It was initiated by Texan President Mirabeau Lamar, who in that time wanted to consolidate the Republic of Texas as a continental power. However, the plan resulted in failure as they would be imprisoned and kept in that state by New Mexican Civilians.

IF you're talking about the war, then

Civilians did things such as mend clothing for soldiers, make ammunition from household silver, and many women followed their husbands to the battlefield where they washed, mended, and cooked for troops. Very few were able to fight in combat, but some women did.