I have an overpayment of social security tax, and the software said that my employer may owe me money. The overpayment is in my refund, what would my employer owe me?

It depends why your social security tax was over withheld. 

If one employer messes up the math or over-withholds, you do not enter this on your tax return. Instead, the employer should give you a refund of the excess social security tax withheld. For example, if you worked the entire year for Employer A and you earn $220,000 and rather than ceasing to withhold Social Security taxes after your wages surpassed the limit, they kept withholding, you would have to get a refund of the excess withheld from your employer. They should then issue a W-2C that shows the correct withholding, which for this year is a maximum of $8,853.60.   

On the other hand, if you worked for more than one employer and you had social security tax over-withheld because one employer did not know how much the other employer withheld, that would be refunded to you on Schedule 3, Line 11 of your tax return. So if Employer A correctly withheld 6.2% of your $100,000 salary for Social Security and Employer B also correctly withheld 6.2% of your $120,000 salary, it would lead to an over-withholding that would be refunded on your tax return. Neither employer did anything wrong and neither would need to issue a corrected W-2. 

Sometimes, you receive 2 W-2s because you transfer within the company or work for two companies that are subsidiaries of the same parent company. In this case, you may get over withheld because of the second situation. However, the IRS thinks you should get it back from the employer because, according to the EIN on the W-2s, they are the same company. Therefore, they will not include it in your tax refund. If that is the situation, you may have to talk to your employer to see if they can get it sorted out. They would need to issue a corrected W-2 and refund your excess social security.