Edit: It has been discovered that the well-known photographs originally thought to be Capt. Barnes are actually of Major Thomas Martin of the 13th North Carolina (see article Here). I have replaced the above photo with the true image of Capt. Barnes.
The following is from Capt. Barnes' Find A Grave profile.
Jesse was the fourth child and third son of Elias and Mahala Emma Sharpe Barnes. After he was born, the couple had six more children who reached adulthood. Growing up on the family's plantation, Jesse was well educated locally before attending the University of North Carolina at Chapel Hill. He started university at age 16 and graduated just before he turned 20 in 1858. By 1860, he worked as an attorney at law in Wilson, North Carolina, near his family home. His older brother Benjamin, also a lawyer, served as the city's mayor that year.
Politically ambitious, Jesse was a staunch supporter of secession. He helped recruit members for the Wilson Light Infantry in the spring of 1861, before North Carolina actually seceded. This militia unit eventually became Company F of the 4th North Carolina Infantry with Jesse serving as the company's captain.
After spending the months after First Manassas until March 1862 at Camp Pickens in Manassas, the regiment saw its first major action at the Battle of Seven Pines. Here they successfully attacked Casey's redoubt, a Union stronghold. Leading his men up the breastworks, Jesse was killed in action. The regiment's commanding officer Bryan Grimes mentioned in his report that "no braver man was killed that day than Captain Jesse Barnes of Company F."
As requested in his will, that he had made out only six weeks earlier, Jesse's body was returned home and he was buried in the family cemetery, next to his father Elias.
Jesse's younger brother William remained in the 4th North Carolina, later transferring to Field and Staff as adjutant and then aide de camp for Bryan Grimes. He survived the war.
After the war, the Wilson camp of Confederate Veterans, later Sons of Confederate Veterans, was named for Captain Barnes. He is also named in the memorial for the war dead of the University of North Carolina.
Edit to add: Here is the link to an article on him in Military Images Magazine: