Pocket Bibles were NOT issued to soldiers when they were muster in by the military. However, there were Bible Societies in both the North and the South which distributed these types of Bibles to soldiers during the War. I have one of these society Bibles that was carried by a soldier in the 9th Arkansas Inf. during the War.

There are presently reproductions of these Bible Society Bibles, both the Union Version, which you appearently have, and one printed in the south in 1862, that can be purchased at some of the National Military Parks (Gettysburg, Shiloh, Vicksburg) Battlefields giftshops.

Your Bible sounds a little unusual, probably purchased, since it has a clasps.