However, I do believe that Garland's Texas Brigade did engage the Union landing party downriver from the fort on the north (fort side) of the river on the first day and made a fighting retreat of sorts back to Fort Hindman and those entrenchments. Garland may have dug some trenches on the north side of the river away from the fort for that purpose.
As far as I am aware the Confederates at Arkansas Post did not have entrenchments across the river on the south side.
However there is a possible explaination. Walkers Texas Brigade of 5 to 6,000 men did march to the assistance of the embattled Fort Hindman Garrison. They did arrived about the time that Fort Hindman surrendered, about a mile above the Jordan planataion and South Bend crossing of the Arkansas on the south side of the river.
It is quite probable that these trench that is spoke of were defensive works dug by the Union Troops on the South side to defend the troops transports from Walkers Texas Confederates. Appearently there was a sort of standoff until about the 17th of January. Wallker made no aggressive attempt against any Union forces. But did fall back to the Douglas Plantation to build a defensive fortification there to protect the Arkansas Post to Pine Bluff road. You will find these fortifications mentioned in Blessingtons account as "Camp Freezeout" and "Camp Skedattle".