Many types of Yagya are described in our scriptures, some are very famous and common, such as Ashwamedh Yagya, Agnishtom, Vaajpeya etc etc while some are not so common and famous. (see many types of Yagya here) But there are two Yagya which are completely different from these common and famous Yagya. Why are they different? Because the material of their Aahuti (offering) is not normal. These two abnormal and uncommon Yagya were performed by Maharshi Paraashar and King Janamejaya. Maharshi Paraashar performed the Raakshas Yagya in which he offered the Aahuti of Raakshas and the King Janamejaya performed the Sarp (snake) Yagya in which he offered the Aahuti of Sarp.
Paraashar's Raakshas Yagya
Paraashar was the grandson of Maharshi Vashishth Jee. Vashishth had a son named Shakti who was killed by a Raakshas employed by Vishwaamitra. When Shakti was killed, Paraashar was not yet born. Vashishth brought his daughter-in-law to his Aashram and Paraashar was born there, so he took Vashishth Jee as his father. At one time, in front of his mother, he called Vashishth Jee "father", then his mother told him that he was not his father, but was his grandfather. And when he heard the account of his father's death, he decided to perform Raakshas Yagya.
He did it and Raakshas started falling down in that Yagya fire. Most Raakshas were burnt this way. Then Pulastya Rishi came and told him that his father died of his own destiny, ao why was he killing innocent Raakshas? Then only he stopped his Raakshas Yagya.
Janamejaya's Sarp Yagya
This Yagya was also very uncommon in itself. There were two people looking at the burning and reviving of the banyan tree from behind a tree. (read the account of death of Pareekshit here) They went to Janamejaya, son of Pareekshit, and told the whole incident to him as how Takshak did not allow that Braahman, who wanted to save him, to come to Pareekshit . Hearing this Janamejaya filled with rage and decided to burn Takshak in Yagya fire. He organized a Sarp Yagya and the Sarp started falling in the Yagya fire.
Seeing this Takshak got frightened and he went to Indra for shelter. Indra gave him shelter. He clung with a leg of his throne. When some time passed and Takshak was not seen anywhere, he asked "Where is Takshak?" Then he came to know that he was clinging to Indra's throne. So he invoked Indra to fall in the Yagya fire. Now with Indra's throne Takshak also started falling. Seeing this Takshak left the leg of Indra's throne, but still he kept falling down. At the same time Aasteek, who was born for this purpose only, came there and stopped this Yagya and saved Takshak.
Thus these are two very uncommon Yagya described in our scriptures. Janamejaya's Sarp Yagya is given in very detail in Aadi Parv of Mahaabhaarat, but Paraashar's Yagya is not found in detail.