If a parent don't attempt to have anything to do with there child, as in phone,write or child support is there a law of some type of abandonment law?

There are laws against leaving a child without adult supervision. A few states have laws that require a parent support their child.

All states allow a parent to ask for support from the non custodial parent.

But you can't force a parent to be a parent. You can't require they call, write, visit or otherwise contact their child.

What is it you want to accomplish?