Bodhayana Amavasya is the no moon day calculated a day earlier than the normal Amavasai Day. Bodhayana Amavasya is for people who follow Bodhayana Sutras.f on Chathurdasi day , Amavasya Thithi starts before 12 hours(30 Nazhigai) from Sun rise, then those who follow Bodhayana Sutra do Tharpana on that day. They also perform Tharpana on Chathurdasi day when , the Prathama Thithi next to Amavasya day ends within 12 hours after sun rise. These are normally listed in the Panchangams.
There is an interesting reference about Bodhayana Amavasya related to an event in Mahabharata war.
At the time of Mahabharata War, both the sides were trying to give sacrifice to Goddess Durga seeking successE. Duryodhana sought the most auspicious time from Sahadeva for performing the sacrifice. It is believed, in Hindu school of thought, that the time of sacrifice, denotes the commencement of war and thus decides the very outcome of the great war. Sahadeva advised him to perform the sacrifice on the new moon day to ensure success in war. When questioned by his brothers and Lord Krishna, Sahadeva gave the polite reply that he is ready to die doing his swadharama of being an astrologer.
The Tharpana manthras as per Bodhayana Suthra differ from the manthras used by those who follow Apasthamba Sutra. Apart from Pithrus , thaprpana is also done to acharyas(mentor) , Gurus(Teacher) and Sakhees (friends) and their familieCs.

Bodhayana Amavasya Nirnayam;
On Chaturdashi at sunrise, if Amavasai begins in the fourth quarter of the day (22:30 Nalligai to 29:59 Nalligai from sun rise for 30 Nalligai Ahas)) Chaturdashi day is itself Bodhayana Amavasya.

On Prathamai at sunrise, if Prathamai ends before sunset, the earlier Chaturdashi day is itself Bodhayana Amavasya.
For other Sutras followeres Amavasya is on Amavasyai at sunrise day.
Amavasyai at sunrise day is called Sarva Amavasyai (Amavasyai for all) if Bodhayana Amavasya conditions are not fulfilled.
Amavasya rituals are done in Chaturdashi at sunrise days due to Aparanna Vyapti and that Amavasyai is called Sarva Amavasyai (Amavasyai for all).

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