Were John the Baptizer and Jesus cousins?

[TonyChanYT]

Yes, according to King James Bible, Luke 1:

36 And, behold, thy cousin Elisabeth, she hath also conceived a son in her old age: and this is the sixth month with her, who was called barren.

Not exactly according to New King James Version:

Now indeed, Elizabeth your relative has also conceived a son in her old age; and this is now the sixth month for her who was called barren.

HELPS Word-studies:

4773 syggenḗs (from 4862 /sýn, "identified with" and 1085 /génos, "offspring") – properly, offspring, a relation; a relative, kinsman (of the same stock).

Thayer's Greek Lexicon:

of the same kin, akin to, related by blood …
in a wider sense, of the same race, a fellow-countryman

John and Jesus were likely related but we don't know exactly how close.