great month of all months - Margasira - for shradha and fasting

 Margasira - which comes after karthika

It is believed that performing pitra puja on this month gives peace and salvation to the soul of ancestors.

Those who were not able to perform shraddha can do tarpan on the amavasya of this month for salvation of dead ancestors

People who have pitra dosha in their kundali, devoid of pleasure of a child, or when Rahu is debilitated in the ninth house should definitely observe fast on this amavasya. Fulfillment of this fast gives desirable results. As per Vishnu purana by fasting on this day

one can please lords Brahma, Indra, Rudra, Ashwini kumar, Surya, Agni, birds, animals, and evils can be pleased along with dead ancestors ...

if one doesn't know the month of a persons death then they can do shradh on this month.

taking baths in a river is considered extremely sacred during this month