If by “interim support” you mean child support, then no, your appeal does not automatically stay the trial court’s child support ruling. On the contrary; as per NCGS 50-13.4(f)(9), the order is enforceable via contempt proceedings in the trial court during pendency of the appeal.
If you want to try to have the payments suspended during your appeal, you first need to move the trial court for a stay. The likelihood of this motion being allowed is pretty close to zero. If you’ve stopped making payments, the other side will likely move to have you held in contempt. At this point you can move the Court of Appeals for a temporary stay and simultaneously petition it for a writ of supersedeas. If you’re found to be in contempt, your appellate paperwork would also need to request a stay of the contempt order. The odds are not in your favor here, either.
Unless the trial court did something so crazy that it’s clearly beyond the pale of reason, your best bet is to make the periodic payments while your appeal is pending. If your appeal is successful, the appellate court’s decision will correct the errors of the trial court and you’ll receive credit for any overpayments you may have made. The situation you definitely don’t want to find yourself in is to have lost an appeal and still owe a whole bunch of money.