ADAH has county files concerning militia service exemptions. For example, all civil officials in each county were exempt but needed to have a certificate on file with the Secretary of State and/or Governor's office. These files contain all that correspondence and more.

Joshua Davis appears in the exemption file for Calhoun County AL. Goshen is (or was) thirteen miles from the Calhoun County courthouse at Jacksonville AL. He as a county constable and exempt from military service on that basis. Each county beat elected constables and JPs, so Joshua Davis may have been discharged from Capt. Stewart's company based on a certificate of election. If I'm not mistaken, state elections should have taken place in November 1862.