Child support and custody..help?

hi im 19 years old and my daughter is 3.. okay heres the thing.. when i was pregnant my exboyfriend denied my child and said he wasnt going to take care of her.so when she was born ..at 2 months ive moved in with him and he would always fight with me and harras me that he was going to take my kid to his country..mexico..he threaten me and always tried to hurt my little one.. i left out of the house and i put child support on him and i took him to court. in court i was put as full custody and he has to give me child support..im a very good mom..i love my daughter shes so special to me .. im very responsible for my age..i take her to her appointments and falowing check ups..i buy her everything she wants..aka spoil and i kno its bad but shes my first child..shes a very happy healthy 4 year old and active..she loves me and i love her..we say it to eachother all the time..lol..i take her to school and bascially dedicate my self to her..well now to both of my gurls because i have a newborn and im married with a very responsible men that loves and cares about my children and has been with my gurl since she was 7 months old..my daughter loves him..now that my daughter is older her dad wants to take her away and wants me to give him child support which i think it isnt fair..because i never denied her and i never left her side.and now that shes older he wants her..i dont smoke or drink i dont go clubbing and leave my child alone i dont hoe around i dedicate my life to my kids..i have a job i go to school and i spent my time with my kids..is ther any chance in him winning the case and getting my child taken away..what are the chances and ways i can get her taken away..because its deppressing and i dont want that to happen..also whats joint custody..