my brother is getting a divorce and we are trying to find out if he is reponsible to pay child support for his stepdaughter when her mom is initiating

Your brother is only required to pay child support for his children. Unless he adopted the stepdaughter (or signed up as the legal father), she presumably has her own father that should be supporting her. If he wants a more detailed answer, he should see a lawyer (particularly if he is going through a contested divorce!)  Good luck.