Uttarakalamrita mentions that Lord Parshurama was born on Akshaya Tritiya.
The auspicious day known as Tretadi or beginning of the Treta Yuga, or
when the birth of Parasurama is celebrated is the 3rd lunar day in
the month of Vaisakha (April-May)-Akshaya Tritiya.
[39, Kanda 2, UTTARAKALAMRITA (OF KALIDASA)]
Firstly need to understand the Method to Calculate Chaughadia Muhurats
First each day is divided into two time periods:
day time (Din-maan) - the period from local sunrise to sunset
night-time (Ratri-maan) - the period from sunset to sunrise (next day)
Each time period contains eight Chaughadias. To calculate the duration of each Chaughadia, the ...
It comes under mundane Astrology. Sometimes a horoscope is delineated considering location such as Sumeru or Vindhyā at other times, specific verses from Brihat Samhitā, etc. are interpreted. You can look at this research paper to know how it is carried out in the later case.