I have heard that (in USA) in case you have a family member who have studied in a university, you may have a higher chance of admission for such university.

Specifically, my mother has studied in Cornell during her PhD studies and I am planning to apply to Cornell LLM. Of course I am not depending on this but I am curious whether it has any effect at all.

Any answer would be very much appreciated.

I'd hope that nepotism would play no part, it doesn't say much for the department if it does!

However sadly nepotism does play some part and it is not unknown that roughly 20% of all intake for the top US universities could be partly attributed to familial relations.