I have recently accepted a job with a company that has paid me to move
to relocate to another state. The terms are if i quit the job before a
year of employment, I will have to repay the relocation amount they
have paid me.
How to professionally deal with this situation?
I assume there's nothing to deal with at this point in time.
You accepted their terms of employment already, so going forward the professional thing to do is to either stay for a year, or repay the relocation amount upon leaving earlier.
Will the employer file a suit against me? What are the repercussions?
They may well sue you. I worked for one company that had similar relocation terms. They did sue an employee who left after 3 months. That's the only time I know of where an employee refused to return the money. All others acted professionally.
This won't be a worry at all if you just abide by the terms you signed. And obviously, if you didn't want to abide by those terms you should have refused the relocation pay or negotiated some other arrangement. That's the way to remain professional.