I dislike it when someone doesn't even respond with an "I don't know," and now I find that I'm guilty myself. I'm sorry.
I don't believe your John T. Alexander could have been James Sr.'s child, and he wasn't the child of Matthew or James Jr., the only two sons for whom I have full families. It's also unlikely that he was the son of their brother William because William was probably in Logan County KY with Matthew before 1796. James Jr., Matthew, and William probably had other brothers who may have remained in SC, but I have no verification of this.