Who's A Jew ?

It is the teaching of Halakhah; 1, The offspring of a Jewish woman and a non-Jewish man is with out question a Jew, even if the Jewish mother is a converted Jew and not ancestral. 2. The offspring of a Jewish father and a non-Jewish mother is without question a Gentile, regardless if he is a converted Jew or ancestral Jew. Does the patrilineal line have any influence in determining the Jewishness of his child? Does the Torah support this?