Thanks for your reports.
I believe the relevant line is the last one in the last report
"where I found Colonel Sill, who had arrived the night previously and fired on the enemy as they were retreating. I inclose Colonel Sill's report."

I am pretty sure it was Sill who took the Cavalry and some infantry east of Piketon and "fired on the enemy" along what is now Burning Fork Road.
It must have been there that William Barker was killed if we are to believe the first hand account of Green Gevedon. Gevedon claimed that several Union Cavalry were knocked from their horse, but no mention of it was made by Nelson.

If Sill reported no Union wounded or dead in that skirmish on the 9th before entering Piketon then perhaps Gevedon mixed up the Burning Fork with another engagement.
The key should be Sill's report. Do you know where I can find that?

Thanks again for your help.
GB