I owed arrears child support but during that time and present, child leaves with me, what are my chances to wipe out back child support as I fully supported my child.
Unfortunately, you have to have a court order to revise or to terminate a child support order. That is true even if you had custody of the child in question.
You may be able to get your attorney to file a motion to modify the child support to reflect the change in custody.
Family Law Attorney
You should file a motion to modify your prior order as soon as possible. The modification can't be made retroactive from the filing date, so the sooner you file the better. If a motion for enforcement is filed, the Texas Family Code allows you to plead as an affirmative defense that the other party voluntarily relinquished possession and access to you. But until you get the court involved, your arrearage and interest will continue to grow.