Jeremiah the prophet's father was
Hilkiah.
Jeremiah 1:1
The words of Jeremiah the son of Hilkiah, of the priests that were in Anathoth
in the land of Benjamin:
Hilkiah was a Levite priest

The Jeremiah spoken of in Jeremiah 35:3 is not Jeremiah the prophet, but he
is a Kenite (son of Cain):
Jeremiah 35:3
Then I took Jaazaniah the son of Jeremiah,
the son of Habaziniah, and his brethren, and all his sons, and the whole
house of the Rechabites;
1 Chronicles
2:55 And the families of the scribes which dwelt at Jabez; the Tirathites, the
Shimeathites, and Suchathites. These are the Kenites
that came of Hemath, the father of the house of Rechab.
Therefor, Rechabites are Kenites,
sons of Cain.
Also, Jeremiah, the sone of Habaziniah is a Kenite, Strongs number 7014
Hebrew, "a son of Kain (Cain)). Strong's number 7014
Qayin, kah'-yin;
the same as 7013 (with a play upon
the affinity to 7069); Kajin, the
name of the first child, also of a place in Pal., and of an Oriental tribe:- Cain,
Kenite(-s),
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