The paternity was established for my son at 6 months of age.. will the father have to pay the past 6 months?

Normally support is payable to the time that the motion was filed in court for support.
So if you file the motion sooner and did not get the test till then,

But it is not "getting out of" support is just not due or owed, till there is a court order.

When was a petition for support filed?