Can a police in Ohio issue a citation on private property you?

Depending on what it is, yes. Driving with no licence or seatbelt, they can do nothing about IF IT IS ON YOUR PRIVATE PROPERTY. Sound violations, maybe.

You'd have to check your local area for specific information, but generally, police can do nothing unless they see a crime being committed such as assault.

As for drugs, the officer must see or have reason to believe there is something wrong. An officer is never allowed to enter a home without consent of the owner/resident or without a warrant.