Father of child threatened custody

[Rina30]

The father of my year old child has threatened to go for custody. He is not on birth certificate and has not provided for his kid at all. I've soley taken care of my kid alone with the help of my parents. He is an alcoholic and a drug user, i fear for the safety of my kid if i was to let him take my kid even for a day and also has been threatening my father . I've saved all the messages and have not ever told him he can't see his kid. Should I be worried ?