|We must've been through hundreds of books already and we can't find him anywhere —|
The knife was first seen in Bob Ogden's memory during the first lesson between Harry Potter and Albus Dumbledore. In the summer of 1925, Ogden was sent to summon Morfin to a hearing for attacking Tom Riddle Snr, a Muggle with a spell that covered his face in hives. As head of the Department of Magical Law Enforcement, Ogden visited the Gaunt shack to investigate Morfin's use of magic on a Muggle. Upon first meeting Ogden, Morfin held the knife brandished in one of his hands, and with his wand he cast a jinx that caused yellow pus to flow from Ogden's nose.
Morfin was seen using the knife again when he was threating to attack Ogden for firing a Revulsion Jinx at his father, Marvolo Gaunt when he was throttling his daughter Merope after hearing that she was in love with the Muggle her brother attacked. It is unknown what happened to the knife when Morfin and his father were imprisoned in Azkaban, but it was presumably left at home as prisoners are not allowed to have wands, and certainly not Muggle weapons either. When Morfin was a free man again he reclaimed ownership of his knife.
During Harry and Dumbledore's third lesson, they dove into Morfin's memory in which he met his nephew, Tom Riddle, who later became Lord Voldemort. Riddle entered the shack and at the very moment Morfin saw him, he thought it was his Muggle brother-in-law since Riddle resembled his father so much. Morfin brandished the knife at Tom Marvolo Riddle, but when he spoke in Parseltongue Morfin stopped.
It is unknown what happened to the knife after Morfin was sent to Azkaban again after being wrongfully convicted by the Ministry of Magic for the murder of the Riddle family. It may still remain in the ruins of the Gaunt shack.