In the Roster of Ohio soldiers, you will often find someone listed as a “substitute.” These were men who took the place of a draftee and were paid accordingly.
Since the draft did not begin until later in the War, this practice was more prevalent in late 1863 and 1864 and usually only effected the Regiments who were in existence since the beginning of the War but had lost personnel due to disease or 3 year enlistment expirations.
Typically, these substitutes were men who had not been chosen in the draft. A cottage industry sprung up of men who enlisted as substitutes, got their money, deserted at the first opportunity only to show up in another area and start the process all over again.
Ancestry.com has a data base on men who were eligible for the draft in Ohio – but it does not indicate if they were actually drafted in that data base.
Martin