Asara B'Tevet

The Tenth of Tevet (Heb, Asara b'Tevet) marks the day on which the Babylonian siege of Jerusalem began in the year 588 BCE, an event which eventually led to the destruction on the Temple in 586 BCE and the first exile from Israel. Though the day usually falls out near the time of Hanukkah, the two holidays have no significant relationship with each other. The Tenth of Tevet is considered a "minor fast" and orthodox Jews refrain from eating or drinking from sunrise to sunset on the day of fasting.

To learn more about this day:

https://www.myjewishlearning.com/article/tenth-of-tevet/