In the fresh petition filed in the US District Court of Massachusetts, the identical twins, Cameron Winklevoss and Tyler Winklevoss, and their Harvard classmate Divya Narendra claimed that Zuckerberg hid critical information from them during the settlement in 2008.
Meanwhile, Facebook rejected the fresh claims saying that these are just "baseless allegations".
"These are old and baseless allegations that have been considered and rejected previously by the courts," Facebook said.
Earlier, the trio decided not to move to Supreme Court with their case that accused Zuckerberg of stealing their idea. Winklevoss twins and Divya alleged that Zukerberg stole the idea of Facebook from their company called ConnectU while at Harvard.
In 2008, the trio agreed a $65 million settlement with Zuckerberg, but later challenged Facebook founder saying that he had misrepresented the value of company stock. They argued if Facebook had revealed their actual market value, they would have received more Facebook shares as part of the deal.