Abner B. Palmer was born on September 2, 1836, in New York to Comfort and Jane Palmer. His father was a farmer who owned $1,500 of real estate by 1850. The family moved to Preston, Pennsylvania, in the 1840s, and Palmer attended school there. He married a woman named Harriet in the 1850s, and they had at least two children: Francillia, born around 1857; and Frank, born around 1859. Palmer worked as a farmer, and by 1860, he owned $200 of real estate and $200 of personal property.
He enlisted in the Union army on October 2, 1861, and he mustered in as a corporal in Company A of the 56th Pennsylvania Infantry on October 16. According to his service records, he was 5 feet, 7 inches tall, with dark hair and dark eyes. The regiment took part in the Battle of Antietam, the Battle of Fredericksburg, the Battle of Chancellorsville, the Battle of Gettysburg, the Overland Campaign, the siege of Petersburg, and the Appomattox campaign. He eventually earned a promotion to sergeant and then to 2nd lieutenant.
He apparently did not vote in the election of 1864. As he explained to his mother, "I did not hav time to go to election & I dont now as they would let me vote if I had[.] I hav no papers to show that I hav pade a tax...I hate to loos my vote but if I do it wont amount to mutch[.] I persume some think that I will vote for Mc [McClellan] seeing I said that I would not for AB [Lincoln]." Nonetheless, Palmer insisted that "eney one that thinks me a Copperhed is mistaken." He mustered out on July 1, 1865.
He returned to Preston after the war and resumed his work as a farmer. His wife probably died in the 1860s, and he married Mary Kellogg in the 1870s. They had at least two children: Jane, born around 1878; and Ada, born around 1880. He died in Preston on February 4, 1885.