You should ask a doctor, because these answers are incorrect. A sociopath is not mentally ill, anyway, as far as I know. You would know if you have it by now, you would be "different" and without a conscience, as far as I know. Anyway, ask your doctor next visit.
Actually, it depends on your personal definition of sociopath as it applies to your father's mental illness. While the previous person answered somewhat correctly, there are definitive properties of mental instability that can become inherited, for example, bi-polar disorder.
I think it is only a small poasibility... One of my uncles are a sociopath... But no one else that I know of in my family have that problem... Don't worry about it, just continue in life... If you want to avoid it I suggest you help people alot and be caring... If you feel like your empathy is draining out you can see a therapist...
Don't ask strangers about something personal and expect a perfect answer. Don't ask a stranger a question a doctor could answer. If you have ANY kind of serious mental health issue, talk to a qualified specialist. Read up a lot, too.