I have Alexander Johnson enlisting the same day in the 93rd as William Johnson. According to Ancestry.com, The New York Adjutant-General’s report has him enlisting as a corporal in Co. C, 93rd Infantry Regiment on 28 September 1861, discharged for disability at Newport News, VA on 21 May 1862. (Ancestry has him in as Johnston, a typo)

The History of the 93rd Regiment580 agrees on his enlistment, says he was appointed corporal Jan 1 1862, discharged May 21 1862 on surgeon’s certificate for disease.
p. 185: Johnson, Alexander. Age 24. Co. C, Minerva, en. Sept. 28, ‘61, ap. corporal Jan. 1, ‘62, dis. May 21, ‘62 on sur. certif. for disease.580

Ancestry.com lists an Alexander Johnson as enlisting on 12-31-1861 at Potsdam, and reupping 7-23-1863. He was discharged first for injury. But he was 18, and the one who enlisted at Minerva was 24 and doesn’t show up in Ancestry’s database. Need to check the rosters of the 93rd.

The Civil War Pension Index at Ancestry.com shows an Alexander Johnson with a widow’s pension filed Aug. 23 1863, application # 308059, certificate #204708, by Amelia P. Johnson. His service is simply given as Ord. Sgt. U.S.A., no unit, so this may or may not be the same Alexander Johnson.75