It's a commemorative service medal for Troop C, New York Volunteers, for their service in Puerto Rico. The Auxiliary Corps was usually an organization of the wives of the regiment. The three locations around the upper obverse are the three main actions of Troop C.
Here's a link to the New York State Military Museum site, which has a capsule history of Troop C.
Regimental medals for Puerto Rican service are unusual, but do appear in the market in the $125-150 range.
OMSA 1136/DM 16