I'm guessing you already know, but the 1850 US census shows the parents of Jeremiah T. Skinner (b. 1828) are Thomas (b. about 1798 in GA) and Frances
Darby Skinner (b. 1807-09 in GA). By 1850, Jeremiah has already reached adulthood and is no longer in the household of his parents, but the 1850 US census shows a number of younger siblings, still living in the household of the parents. Let me know if you need that information.
I know this is not related to his Civil War service, but perhaps it is a date you need.
The Daily Constitutionalist. (Augusta, Ga.), February 28, 1875, page 1.
Here is the record showing where Jeremiah Thomas Skinner was serving in 1862 -- on the Alabama and Tombigbee River repairing gun carriages.
@ucvrelics will be able to tell you where this was and what it entailed.
Notice that he signed the second and third one as "Jere T. Skinner" --- so he went by "Jere" aka Jerry
Here are records for your Jeremiah Thomas Skinner, age 37, serving as an artisan at the SC Armory Macon GA. These records are filed under "miscellaneous" Confederate records.
And the records for J T Skinner working as a carpenter at the Macon, GA Armory August 1863 to December 1863.
And the records showing that he enlisted on Oct 8, 1863 and served as a Private in Co A of the Armory Guards, Macon GA
And the record of his capture and parole April 20/21, 1865 at Macon GA
And this one for a "J T Skiner" working as head mechanic at Salisbury NC in March 1864. It is possible that he was sent to NC for some assignment and then wound up back in Macon later, but it would require additional research to determine if this man is your Jeremiah Thomas Skinner.
Since "S" and "L" are often mistranscribed, I decided to attach this miscellaneous record too. Jeremiah had a younger brother, James S. Skinner (b. 1836 in GA) It is possible that this record is for James -- detailed as a carpenter at Macon, GA