My daughter's father is taking me to court for visitation rights... but I don't understand how the main reason he is illegal but beside that he doesn't ''provide nor support'' her. Since 2006 I've received maybe a total of 8 payments of child support and owed over 4000.00 and I have called child support but am ready to try what ever I can do because if he gets the ''right'' to see her then he should have to support her also.

Unfortunately the law doesn't view it that way. Most states, including Ohio, keep support and visitation as separate issues and treat them totally separately. So he can apply for and get visitation despite his being in arrears on support.

What you can try to do is hammer the courts to enforce the support order, to the point of putting him in jail if he doesn't pay.

Merely oweing child support has nothing to do with visit rights. He can and has rights to visit the child. If you are not allowing him visits ( if they are court ordered) you could be in as much issue or trouble as he could be for non payment.

Is there already a child visit order in place.
If not he will be awarded one.

Next you can not "issue a warrant" depending on the state merely being behind 4000 may not be enough to be arrested, he could lose his drivers license. You can take him back to court for contempt in a counter claim to his vists, but these are two separate issues.

He may or may not be found in contempt, but may have to agree to some payment plan, he will although be given visits with his kids

As Scott said, support and visitation/custody are two separate issues. He is the father; he is entitled to see her. If you want to fight visitation you have to PROVE he is a danger to the child.

I would also file for a new support order and, if he has not paid in accordance with an existing order, request that he be held in contempt of Court.