Can a father be prevent from seeing his child because he has not paid childsupport?

In alabama child support and visitation are two separate issues. Since they have nothing to do with each other, a parent cannot legally be prevented from seeing children for not paying child support.

As a general rule participation by the non-custodial parent is to be encouraged. As a result the issues of child support and visitation are viewed separately. That is, if a father can be prevented from exercising his visitation rights because he is not paying child support, it follows that the father need only stop visiting the child to terminate his child support obligation. Of course, if a father were able to do this every state would face a catastrophic chore of providing for single parent households. Fathers are meant to provide support, whether or not they exercise visitation rights---and fathers do not lose their rights as a parent simply because they fail to pay. The courts have ways of compelling payment apart from severing ties between biological family members.

Enforcement of the Child Support Order in Alabama-child support and visitation are two issue's and one cannot be used against the other. Howevr child support services have ways to enforce the non-custodial parent to pay his child support.
I have enclosed the laws on enforcing child support in your state.

Child Support Enforcement (CSE) offices help with collecting the money due no matter where the non-custodial parent lives. When a parent has disappeared, it is usually possible for the CSE office to find him/her with the help of state agencies, such as the Department of Motor Vehicles, or the Federal Parent Locator Service. Your caseworker will tell you what information is needed to find an absent parent or his/her employer.

Enforcement includes intercepting Federal and State Income Tax refunds, liens on real and personal property; orders to withhold and deliver property; or seizure and sale of property.