The earliest mention of the purushamriga is found in the Yajur Veda. The Yajur Veda is the second of the four sacred texts that are considered the foundation of contemporary Hinduism. The Yajur Veda is related to the performance of ritual. The Yajña or Vedic fire-sacrifice is the central subject of this ancient text.
Another ceremony that was of great significance in the ancient Vedic civilization is the ashvamedha or horse sacrifice. It was one of the royal ceremonies, and only kings could perform it. Its performence took the duration of one year, and it incorporates much astronomical symbolism.
The purushamriga is mentioned as one of the wild animals dedicated to various deities at the ceremonies that form the benediction of the performance. It is mentioned specifically as being dedicated to the Moon in the following verse. The following is the verse from the Krishna Yajur Veda, in the Taittiriya Samhita recension, The translations is from A.B.Keith (1914)

“Purusamrigascandramase godhakalakadarvaghatah te vanaspatiname
‘tyahne krsnoratrye pikaha ksvidkanila sirsni te ‘ryamne dhatuh karkatah”

Translated this means

“The human beast to the Moon; the lizard, the Kalaka, the woodpecker,
these are for the trees; the dappled (deer) to day; the black (antelope)
to night; the cuckoo, the Ksvinka, the black headed, these are (to be offered)
to Aryaman; the crab for Dhatr.”

For a more detailed discussion of the purushamriga in the Veda, click the link 'In the Veda' on the left.
Although the Vedas and the Vedic sacrifices are still an sgnificant element in Hindu doctrine and practice, over the millennia the worship of the divine in temples through agamic ritual also gained an important role. Today this form of worship is significant for contemporary Hinduism. In this form of worship, the divine energy is invoked in a murti or icon through ritual. In this temple tradition various rituals are performed as a part of daily and yearly ritual cycles according to the doctrine. The purushamriga plays a significant role in both these daily and yearly ritual cycles, especially in the temples of southern India.
During the daily ritual cycle of a South-Indian temple the ritual of the 16 honors is performed at significant sacred moments through the day. One of these 16 honors is the diparadhana or lamp ceremony. During this ceremony a series of metal oil and camphor lamps are lighted and offered before the deity. These offers are accompanied by the chanting of appropriate ritual verses or Veda-mantras.
In all temples dedicated to deities that belong to or are related to the God Shiva, this lamp ceremony includes a lamp that features the image of the purushamriga. The offer of the lamp is always accompanied by the chanting of the relevant verse from the Krishna Yajur Veda. For more information about this ritual, click the link to 'In daily temple rituals' on the left.
Festival processions or utsavas form a significant part of the yearly rituals performed in South Indian temples. In most temples such festivals occur once a year, at significant and auspicious astronomical times. These times are calculated with the help of the ritual calendar or almanac. Such festivals can last for ten days or more, with every day having its own special ritual performance, with it own symbolic and philosophical significance and meaning.
Important for the festivals are the processions when the presiding deity of the temple is ceremoniously brought out of the temple and carried around a sacred circuit around the town. Such processions are the high-light of every festival. During the course of the festival, the deity will be seated on various vahanas or vehicles. They carry special symbolic significance within the totality of the festival. And in several temples one of the vahanas or vehicles is the sphinx-purushamriga. For more information about the role of the purushamriga as the vehicle of deities during processions, click the link to 'In festival processions' on the left.
The most abundant presence of the sphinx in Indian temples is found among the sculptural art that forms the adornment of most Hindu temples. Here we find many representations of Indian sphinxes, invariably positioned in ritually significant places. In parallel with the ritual function of sphinxes in other parts of the world, here too the sphinx’s role seems to be primarily apotropaic, that means it is protecting the sacred space and warding off evil. Several temples preserve an oral and textual tradition about the role of the purushamriga as one of the protective demi-gods. That is why we find the sculptures of purushamrigas especially positioned on temple gateways. But also near the shrine of the presiding deity, among the sculpture of the halls in which festivals are celebrated, and variously at other points of ritual significance. For more details, follow the link 'Ritual significance of sculpture'.
My research has uncovered several other significant rituals and festivals that are directly connected to the sphinx-purushamriga. Two of the most interesting and distinctive rituals involving the sphinx include one ritual performed for abundant rain by the people of Tiruvatavur, a village near Madurai in Tamil Nadu.
The other exceptional ritual is the performance of a long run, commemorating one of the most popular legendary deeds of the purushamriga, when devotees run 75 kilometers in 24 hours, visiting and worshipping at 12 Shiva temples situated in the southernmost part of India, near Kanya Kumari, or Cape Comorin.