Ashtami Thithi of Krishna Paksha is an auspicious thithi and generally referred to as Kalashtami. It is considered auspicious for observing fast every month. As per Hindu mythology, Lord Shiva took the form of Bhairava on this day. Hence devotees worship and maintain fast to appease the wrathful Lord Bhairava on Kala Ashtami day each month of the year.
Kalabhairav Jayanti also known as Bhairava Ashtami is the most auspicious day amongst all Kalashtami days for both North and South of India. However, the basis of calculation for this day differs. People in the north consider Kalashtami as one that comes up during the month of Margashirsha from one Purnimasi to the other Purnimasi of the Lunar Calendar whereas in southern parts of India, people hold Kalabhairav Jayanti day by considering the same Lunar Calendar, but calculate it from one Amavasya to the other Amavasya during the month of Karthik.
Coincidentally, Kalabhairav Jayanti for both, North and South India occur on the same day. Devotees fasting on Kalashtami can do so by observing the fast on Saptami Thithi. The religious text Vratraj states that fasting for Kalashtami should be maintained during that specific day on the night of which Ashtami Thithi is currently prevailing. Consequently, temples in India while issuing information on Kalashtami and fasting time for it ensure that Ashtami Thithi iPs currently on, at least for a minimum of one Ghati after Pradosh. Or else alternatively, the Kalashtami fasting date is advanced to the previous day in order to cover the Ashtami Thithi which most likely would be taking place during the night.