How can I file for Establishment over my mother''s estate if I live in another state?

My condolences on your loss. The only advice I can give you is that you should contact an experienced probate attorney who is licensed in the state where your mother had her primary residence at the time of her death, since that is most likely where her estate will need to be opened. That attorney can find out information about the situation and advise you of what steps need to be taken. You could also try contacting the appropriate court directly. However, most court clerks will not provide you with legal advice. Probate and estate administration work is not really something which you should try on your own. Find a good lawyer who can get you started and provide you with at least a set of guidelines, so that you know what things you should be aware of and may need to deal with. The fact that you live in a different state may or may not be a problem - that will depend on where your mother lived and what that state's laws say about non-resident personal representatives. In Georgia, it's generally not a significant problem. In other states, it might be.