In the left corner of the heading is the printed letter B. This was used to help clerks sort cards into letter groups by last name. John Barker's last name starts with the letter 'B', so his cards have the letter 'B' there. That's not his company designation.
Underneath that you read the name, John Barker, Pvt. {Capt. Leonidas H. Elliott's Co., Kentucky Infantry* If we could look at the original muster roll at the National Archives, the top of the roll would read, Capt. Leonidas H. Elliott's Co., Kentucky Infantry. That's the way the roll was submitted to the Confederate War Department. Of course these were later captured and taken to Washington with other Confederate papers.
Down at the bottom of the card, you'll read *This company susequently became (1st) Company D, 5th Regiment Kentucky Infantry (Mounted). All of this was printed by the U.S. War Department many years after the war ended.
For what it's worth, if John Barker was in Federal hands more than once, records should appear in his name in a different service file.