Found this listing of Civil War veterans from Madison County, Indiana with the surname Alderman.
Alderman, James, Private, Co. K, 8th Infantry, mustered 9/5/1861, died at Otterville, Mo. 12/14/1861
Alderman, James W., Private, Co. K, 16th Infantry, mustered 8/19/1862, deserted, Indianapolis, 12/14/1861
Alderman, John, Private, Co. C., 110th Infantry, mustered 7/10/1863, mustered out 7/15/1863
Alderman, Washington, Private, Co. E, 8th Infantry, mustered 4/22/1861, mustered out 8/6/1861 term expired.
Still need to work on these individuals to determine which ones are related to me. Washington Alderman for sure, the others are probably cousins/brothers.