I am receiving child support for my daughter, her father has recently been approved for ssi disability in Tennessee.he has signed her up for benefits also will my child support be takenm away if she gets a check also from his disability?

If he is on SSi then you won't be getting a child support check at all. There is no benefit program for SSi. Only if he has enough credits and is going to be on SSD is there a benefit allowance.

Also if he has no income, how is he going to pay you a child support check ?

Child support is also based on amount he earns,