Thank you for your follow up.
Unfortunately, there is a presumption that both parents share 50/50 custody, however this presumption can be rebutted/changed in court by showing to the court that one of the parent is either unfit to be a parent or to have custody of the children/unsupervised visitation.
While there is no sure way for you to make sure that the father doesn't obtain a court ordered visitation/custody of the minor children, it would be very important for you to document and to report any type of abuse to the authorities such as Child Protective Services / DCF and police.
Also, keep in mind, that if your ex signed the birth certificates, he would be presumed to be a legal father of your other 3 minor children and can file a petition to establish custody / visitation for them and the biological daughter at any time and unfortunately the fact that he has failed to pay child support
, would not be a factor, as under the law child support and child custody / visitation are two separate legal issues that do not effect each other.
Also, if the father fails to visit children for more than 6 months, it would give you legal grounds to file for the termination of your ex's parental rights
based on abandonment and even if the father's parental rights are terminated, he would still be subject to child support obligation for all the children.