Alan and Bill,
A fusiler sounds very European or maybe Canadian to me. I did a search on Mr. Collier. He was a private in this regiment for only 13 days before he was discharged due to a disability. (Short timer?)
There was another Collier, Thomas who enlisted at the same time with Asa. Could they be brothers. Thomas was discharged on March 7, 1863. Also disabled, maybe he was injured at Corinth. Just a guess. That is when Van Dorn attacked the troops there and the 56th was involved in the repulse.