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Georgia law recognizes a cause of action (generally referred to as abuse of process) for situations such as the one that you are describing. If you can show that his claims are frivilous and that he has repeatedly brought fivilous claims against you then you can file the abuse of process claim.
The good news is that if you win the abuse of process claim he must pay your attorney's fees. So while I know that you do not want to go through any additional expense in getting your ex to stop harassing you, if you prevail you will be reimbursed your attorney's fees as well as receiving damages. Although actual damages are often hard to prove, you may be eligible for punitive damages.
These articles discuss the issue in more detail:
I hope this information is useful to you. I am sorry that there is not an easier or simpler way to get him to stop harassing you.
If you have additional or follow up questions on this please feel free to ask.