If you read Fagan's report you will find he states they attacked the fort on Hindman Hill aka Battery D. You will also see that his brigade consisted of Hawthorne's, Bell's, Brooks and King's regiments. There was no Parson's regiment in Fagan's brigade.
Cocke was the Maj in the 39th aka Hawthorne's regiment. I probably inadvertently stated it as Cocke's instead of hawthorne's. It was the same regiment either way.