I've recently resigned from a company in Georgia giving them 2 weeks notice but took a week of final week off using my vacation time. When the final check came, I found that they only paid one week's worth. So I made an inquiry and got the following response from the company:

PTO can not be included as part of your resignation. We only considered your notice to be one week.

This was a surprise to me since I have not seen any company policy describing such claim. Is there any legal ground on this matter?

There is no law on this, it is up to their usual and customary company policy.