As a resident of Tennessee you are not subject to any TN state taxes on wages, however, your income from the state of Virginia is taxable. You will have to file a tax return with the state of Virginia at the end of the year, and while it is possible that some of your taxes may be refunded depending on how much was withheld, you will certainly not get a full refund.
Typically the way state taxes work is that you are liable for state tax in the state where you reside and in any state where you earn income. Normally what would happen is that if an individual works in a different state than where he resides, then he pays tax to that state, but then his resident state gives him a credit for taxes already paid to the state where he works. That way, the same income is not taxed by both states.
However, in your case since TN has no income tax on wages, there is no way for you to claim a credit with the state of TN since you do not pay income taxes there to begin with.
It's unfortunate that you are one of the lucky few who live in a state with no state income tax on wages, and yet you will end up paying them because of working in Virginia.
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