Can I get refund from gorgie state for state tax that my employer deducted from my paycheck since the company is located in gorgie but I did not work and live in gorgie.

We call it GEORGIA here. Did you not notice it was being deducted? You will need to file a GA income tax return and send an explanation letter with the return. Then you will have to fill out a return for the state where you live, if they have an income tax. Have your employer change your witholding to the state where you live.