Krittika, also spelt as Krutthika nakshatram or Karthigai Nakshatram, is the third nakshatram among 27 birth stars in Hindu Astrology.
Krittika is the birth star of Lord Murugan (Subramanya swamy) hence Subramanya puja or Skanda puja is the most auspicious puja to perform on this day.
Aadi Krithigai is one of the big festivals in Tamil Nadu which falls on Krithigai nakshatram in Aadi masam.
Here is the list of the dates of Bharani nakshatra 2021-22 dates
23 January 2021
19 February 2021
19 March 2021