What is the punishment of 3rd offense assault in Texas

An assault can be punished a lot of different ways. To tell you how this "3rd offense" could potentially be punished, you would have to tell us much more about the two previous offenses. If a case has been filed and accepted by the DA, call them. That will be the easiest way to find out. Just ask them what the "range of punishment" is for the case pending against him or her.