Betwixt is a synonym of between that lends an old-fashioned feel to both speech and writing. It is sometimes used in the phrase "betwixt and between" to mean "in the middle" or "neither one thing nor the other."

// Charley took a seat betwixt two other passengers.

// They sat on the long bench, a pile of books betwixt them.

// The novel's protagonist is at the edge of early adulthood, when one is betwixt and between.

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"Wolverines players were skipping toward the locker room after the trophy presentation, roses betwixt their teeth, battle scars on their bodies. Not many players in the recent history of college football have gone to the underworld and come back alive. But there was no doubt they belonged here, at last." — Tyler R. Tynes, The Los Angeles Times, 2 Jan. 2024

Betwixt and between have similar origins: they both come from a combination of be- ("make, cause to be, treat as") and related Old English roots. Both words appeared before the 12th century, but use of betwixt dropped off considerably toward the end of the 1600s. It never fully disappeared, however, surviving especially in the phrase "betwixt and between" ("neither one thing nor the other"). Nathaniel Hawthorne employed betwixt no fewer than thirteen times in The Scarlet Letter, as when writing of "fear betwixt" the young, guilt-stricken minister Arthur Dimmesdale and Hester Prynne, as well as "a kind of horror at her boldness, who had spoken what he vaguely hinted at, but dared not speak." Nowadays, betwixt is uncommon, but it isn't archaic; it's simply used more purposefully than between, as it tends to lend a certain old-timey feel to speech and writing.