Legal Question in Real Estate Law in Georgia

You don't say where you found it, but many states have laws that could led to your prosecution for a crime. Quite obviously, a person with a minimum of basic honesty, morals and ethics would take steps to return the ring to its rightful owner (returning it to the property manager or law enforcement) regardless of what any laws provided. If this is not you, nothing you read here is likely going to matter anyway,

In most states, you are committing a crime. You can be jailed and fined for not turning it over to law enforecement.

You also, in asking, are showing a complete lack of morality.