Legal Question in Family Law in Georgia

No. It is sad that you didn't see a lawyer before making the mistake of a lifetime (never buy a house with a live-in paramour unless you have a contract to address this matter in advance). The few hundred dollars you saved by skipping that step will be very costly now. This is not fixable easily. Unless the two of you reach a compromise, you will need a lawyer, spend many thousands or more on a partition lawsuit, and the result will be a forced court sale at a discounted price where you and he split the profit or loss.

Unfortunately, you have made the mistake of entering into a mortgage with no safeguard in place on how to resolve this type of issue. I assume you are both on the title. Neither of you can make the other leave. You will either have to resolve the issue, and make sure it is in writing, or file the appropriate action and a Judge can tell you what to do. This will be costly. Keep in mind, even if a Judge allowed one of you to keep the house, that party would likely be required to buy out the other parties interest and do whatever is necessary to remove the other person from liability on the mortgage. If neither of you can refinance the mortgage in your name, it is likely the residence would have to be sold.