The Ohio Bureau of Motor Vehicles (BMV) could tell you for certain the consequences of not renewing your OH license plate sticker, which is given to you when you renew your registration.
ORC 4503.11 discusses the requirement of car owner to register their vehicle. Here it states that no person who is the owner or chauffeur of a motor vehicle operated or driven upon the public roads or highways shall fail to file annually the application for registration or to pay the tax therefore.
Subsection C of this Ohio Revised Code goes on to say that whoever violates this section is guilty of a misdemeanor of the fourth degree. This type of misdemeanor in OH can come with not more than thirty days of jail time and a fine of up to $250.
If you were cited for the offense of driving with expired tags (registration) in Ohio you can contact the court to find out more about the penalties you may be facing. It may help you if you go to a BMV office and renew your registration before your court date.