There are five calendars in Vogue in India.
In general there are five calendars being followed in India.
Shalivahana in Deccan,
Tamil in Tamil Nadu,
Malayalam calendar in Kerala and
Bengali calendar in Eastern India.
There are more regional versions of Calendars.
However the two principles are,
1.Follow the movement of the Sun.
This is called Saura Manasa (Solar)
2. Follow the movement of the Moon.
Those who follow the Lunar calendar,Chaandra Manasa have one month extra once in three years.
This extra month is called the Adhik Maas, additional month to align it with the Solar calendar,Saura Manasa.
This month is called Purushottam Mass and is dedicated to Lord Vishnu.
The reason is that Surya is considered to be the Visible Reality,Prathyaksha Brahma.
And he is An Adhitya.
He is one of the twelve Adhityas.
Vishnu is an Adhitya in His manifestation.
He is also the Protector.
Hence the Adhik Maas is dedicated to Him.
‘Extra Month, or Adhika Māsa falls every 32.5 months on an average. It is also known as Puruśottama Māsa, it is said that the name was given by Lord Vishnu as his name to this month. The solar year is made up of 365 days and about 6 hours, and the lunar year is made up of 354 days. Thus there is a gap of 11 days, 1 hour, 31 minutes and 12 seconds between the lunar and the solar years. As this gap accumulates each year, it approximates in three years to one month. No adhik mas falls during Margsheersh to Magh. A case of Adhik Karttik is extremely rare, but in the 250-year span (1901-2150 AD) it would occur once, in 1963 AD.…
The Moon takes about 27.3 days to make one complete orbit around the earth. The earth orbits around the sun once every 365.2422 days (= earth’s orbital speed of 29.79 km per second). The earth and the moon in 27.3 days have moved as a system about 1/12 of the way around the sun. This means that from one full moon to the next full moon, the moon must travel 2.2 extra days before it appears again as a full moon, due to the curve of the earth’s orbit around the sun. Ultimately this creates a variance of 10.87 days a year between a lunar year and a solar year. To compensate for this difference, the additional month is added after every 32.5 months on average.
Just as there are lunar years with the extra month making 13 total months, there are lunar years with a reduced number of months, with only eleven months in the particular lunar year. The lunar year with eleven months is very rare. It occurs once in 140 years or once in 190 years…
A month-long mela (fair) is celebrated in Machhegaun village in Nepal during Adhika Māsa. It is general belief that one can wash away all his sins by taking a bath in the pond at Machhenarayan temple.
Since this is a special month which does not come every year, there are no specific festivals like Dasara or Diwali in this month. Rather this month is treated as special and holy month and many people perform the adhik maas vrata. People perform extra mala japas, pradakshinas, pilgrimages, scriptural reading and parayans.
During Purushottam Maas, people perform various types of religious rituals such as keeping fast, recitation of religious scriptures, mantras, prayers, performing various types of puja and havan. Vratas (fasts) of various durations (full day, half day, weekly, fortnight, full month) are often undertaken. The vratasmay be of complete fasting with liquids only or without liquids, fasting with fruits only or keeping fast with vegetarian food, as the individual can tolerate. It is said that the persons performing good deeds (satkarma) in this month conquer their senses (indriyas) and they totally come out of punar janam (the cycle of rebirth).’
Reference and citation.