The area you are asking about was pretty much bypassed by the war. While there was a lot of troop movements both Confederate and Union along the Pine Bluff to Little Rock Road, and as Skip pointed out several temporary camps around Redfield and Tar Camp, I am not aware of anything that could be classified as a skirmish or larger in the area. There was no Union activity in the area prior to the fall of Little Rock and almost no Confederate activity along this road after the fall of L.R.
There was one incident where 3 young boys captured a steamboat near Tar Camp from its Union Guards and burned the boat. This incident is documented in the Confederate Veterans Magazine written around the turn of the century.