In April 1862, the Confederate Congress enacted a Conscription Act which allowed for the conscription (draft) for three years service of white males between the ages of 18 and 35 who were not legally exempt from service.
Men who were above and below the age limits were permitted to be discharged as "non-conscripts", i.e., exempt from further service.
The age limit was adjusted over the next three years, as were the legal exemptions, but in the last year or so of the war, with things going so badly for the Confederacy, the limitations of the Conscription Act were often given lip-service, or ignored altogether. At that point, particularly in the Trans-Mississippi Department, just about any man or boy who could shoulder a musket was permitted to enlist (though their actual ages were often falsified by the enrolling officers).