Court may divest mother of authority over her illegitimate child

Dear PAO,

I am a father of three boys, ages 4, 7 and 9, with my former girlfriend. My children are with me right now because their mother abandoned them three years ago. Just last week, their mother appeared and tried to get them. Of course, I did not allow this to happen. But their mother threatened to sue me if I will not give the children to her. Can my ex-girlfriend recover the custody of our children from me? What do I do?