Can a business in Ohio withhold a final paycheck from an employee who did not give a full two weeks notice to leave?

No. This violates Ohio and federal laws requiring that employees be paid at least minimum wage for all hours worked. Feel free to contact our office for a free consultation with an Ohio unpaid wages attorney. If your employer works in this manner, there is the potential for other unpaid wages.   Ohio unpaid wages lawyer http://mcoffmanlegal.com/practice-areas/wages-and-overtime/unpaid-wages-and-unpaid-overtime-attorney-columbus-ohio/