Andesite Cobblestone is a block added by Better With Mods. Similar to vanilla Cobblestone, Andesite Cobblestone is dropped when breaking Andesite. The block was added for consistency with vanilla Minecraft's stone. Andesite Cobblestone can be used in place of cobblestone in many recipes.
Andesite Cobblestone, along with other Cobblestone drops from the mod, can be turned off in the config file under the HCCobblestone option.