You cannot deny child custody rights to your ex just because they will not pay child support. For example, maybe your ex, who has visitation rights, is a few months behind on their mandated support payments. When they show up for visitation, you may be tempted to tell them that they cannot see the child until they pay what they owe.
Even though this may feel like a fair way to try to enforce the child support order, that order is independent of the custody order. Just because they violated their support obligations, that does not mean that you can then deny them their custody rights. They still have a right to see the child.
Are there any reasons to deny custody?
You can typically only deny custody if there is a risk to the child. For instance, maybe there are concerns about parental abduction, so you do not believe that the other parent should be alone with the child.
Another example could be if your ex struggles with drug or alcohol use. Perhaps they show up to pick the child up in accordance with the custody schedule, but they are intoxicated. You do not think it would be safe for them to be responsible for the child, and you certainly do not want your child to get into a car with them. In a situation like that, you may be within your rights to deny the custody exchange.
Generally, child support issues do not justify violating a custody order. Instead, you should understand the legal options for enforcing support. An experienced attorney can help you take the right steps.