The object you might be thinking of is the Time-Turner, which is a magical device that allows the user to travel back in time. It was not owned by anyone in particular but was part of the Ministry of Magic's collection. It was used by Hermione Granger in "Harry Potter and the Prisoner of Azkaban" to attend multiple classes at the same time.
It's possible you're confusing the Time-Turner with the Invisibility Cloak, which *is* a real object in the series and is a powerful artifact that renders the wearer invisible. The Invisibility Cloak was originally owned by Ignotus Peverell, one of the three brothers who received gifts from Death in the Brothers Grimm fairy tale. It was later passed down through generations until it was inherited by Harry Potter.