The Union colonel says he approached Clarksville via Blue Springs, 16 miles from Clarksville on the 5th of Sept 1862. On the 6th he engaged the pickets somewhere between 3 to 10 miles from Clarksville near New Province. On the 7th he moved closer to town (about 3 miles) where he engaged the defenders of Clarksville, who retreated and tried to dismantle the Red River Bridge “the only practical approach to town.” The defenders retreated from the bridge toward town and the colonel set up artillery on a bluff “commanding the town.” On the 8th he occupied Clarksville. Sept 7 is called Riggin’s Hill. I’m sure the Clarksville roundtable people will answer you in much greater detail. War of the Rebellion is online.