I have three kids and single mom.they have different father.I don't have a problem with the fathers of my two older kids.the fathe of the youngest wants to have custody of our daughter.he is no longer guving child support because he told me that he does not have custody of our kid.he wants to have our daughter two weeks per month.our daughter is only 2 years old.we used to live together but we did not marry.we got separated because he used to abuse me verbally,emotionally and physically which my parents found out and they asked me to stay with them.can I still file for child support even if ill let the father have our daughter for two weeks because um getting tired of him telling everyone that I'm giving him a hard time spending time with our daughter which in fact I still allow him to see our kid every time he wants to meet up to see our daughter

Its your right to file for child support... its also his right to file for custody (full not just partial).. and as the other parent he has equal rights to have custody as you do. When the court orders custody and visitation... you don't get to let him do anything, nor does he... both of you will have a court order as to what you WILL do... and the force of the court backing it for whatever parent violates it.

So a custody order will be a wise thing to get...

The only way to settle this is go to court and file for support and custody. You will win the support since you would be primary care giver even though he most likely would get weekends and split holidays

She won't necessarily get it... the child is no longer an infant.. so he does have a good chance to get custody (meaning equal)... particularly if he can demonstrate he can take care of her just as well... or better. He's the father... his rights are equal to hers. And many men ARE actually raising their children these days... not sending a check...

But that's up to the court to decide.

Yes he could generally, at least in my state they put heavy consideration in not uprooting the child unless it is ultimately in the best interest of the child's well being.

... can I still file for child support even if ill let the father have our daughter for two weeks [?]...

As others have suggested, you do not get to "let" him have her. It's as much his right to have the child as it is yours.

But what troubles me about your question is that it suggests your purpose in having children is to create a source of income for yourself. Three children with three different men strongly suggests this.