Hello. I may be wrong, but I think you need to post this in Arkansas where they have an active board. You may even want to say
"Attn. Bryan or Doyle" on the posting as those guys know a lot about what happened in Arkansas during the Civil War.
Several more are almost as good about helping.
If I were you, I would ask about a prison that was at Fayetteville. I personally am not aware of one, but that does not mean much.
Make sure you list it like a question and not a genealogy report and you will probably be more likely to get a response you desire.
Good luck.
Linda