Legal Question in Criminal Law in Georgia

Yes.

Sure it is. It is their property. That is what "trespass" is all about.

Sure it is. And if you ignore their warning, you have committed a criminal trespass and can be jailed for up to a year and fined up to $1000. Stay away.

The complex is private property. If the owners don't want you on the property for whatever reason and have told you not to come back then you may not come back. The owners have the right to decide who they do and don't want to allow on their own property. If you go back again after being told you are not welcome it will be considered criminal trespass. You're not really questioning if owners of private property have the right to decide who comes on their property are you?

Yes!!