The Code of Jewish Law clearly states that a child of a Jewish mother is Jewish, regardless of the father’s lineage.
https://www.chabad.org/library/article_cdo/aid/601092/jewish/Why-Is-Jewishness-Matrilineal.htm
In 2013, Biden had a Jewish Sukkah built at his home, by CHABAD
https://obamawhitehouse.archives.gov/realitycheck/blog/2013/09/25/first-vice-presidential-sukkah
"On the holiday of Sukkot, Jewish people spend time in the sukkah."
https://chabad.org/library/article_cdo/aid/609535/jewish/What-Is-a-Sukkah.htm
In 2013, Biden had a Jewish Sukkah built at his home, by CHABAD
https://obamawhitehouse.archives.gov/realitycheck/blog/2013/09/25/first-vice-presidential-sukkah
"On the holiday of Sukkot, Jewish people spend time in the sukkah."
https://chabad.org/library/article_cdo/aid/609535/jewish/What-Is-a-Sukkah.htm