Regarding Child Custody (3 yrs old Girl Child)

I am having 3 year old child. Being a father, I need her custody.And I need separation from my wife. But I cant let her my child go. I stay in USA now. My wife did false police complaint against me for domestic violence ,when I was in in India. It was a complaint not FIR. But I did compromise because of my girl child. When I came to USA ,my wife started seeing somebody else. And I caught her but have no evidences to prove that . Every time she harasses me and my parents and threatens to take my daughter with her. Is there any solution to this ? I need custody of my daughter or whether I have to bear this punishment /harassment from my wife , for the entire life only because of my love towards my daughter? As if giving a birth to a child a crime.I trusted my wife a lot. Even I bought an apartment on her name without taking a penny from her. Now I don't want to live with her . Please suggest if there is any hope to get my child's custody and what are the ways?