Is it permissible to marry the daughter of the third wife of the paternal uncle, if the father was suckled by the first wife of his paternal uncle, and the daughter of the third wife was not suckled by her paternal uncles?

Your father's suckling from your uncle's wife makes him a son to her and to your uncle. Therefore, your uncle's daughter, from any of his wives, is your father's sister through fosterage, meaning she is your paternal aunt. Thus, it is not permissible for you to marry her. And Allah knows best.