Child support and visitation are two separate matters.
If you are ordered to pay child support and aren't she needs to take you to court to have that resolved. If you aren't ordered to pay child support and she feels she needs money, she needs to take you to court for that as well.
If you have a custody arrangement signed by a judge she is required to abide by that, regardless of and independent of the status of your child support situation. Failing to allow you access to your children when there is a court order allowing it is a jailable offense. (she's in contempt of court)
Child support is for supporting the children and paying for their living expenses. It is NOT payment to the custodial parent in exchange for visitation rights.
If she will not allow you to see your children the next time it is your court appointed time, have a copy of the custody arrangement in your hand and call the police.