The powerful jewels sought by Fëanor in J.R.R. Tolkien’s mythology are the Silmarils.
The Silmarils are three jewels made by the Elf Fëanor during the First Age. They contain the light of the Two Trees of Valinor, making them among the most precious objects in Tolkien’s legendarium.
Their theft by Morgoth drives the central conflict of The Silmarillion. Fëanor and his sons swear an oath to recover them, an oath that brings violence, exile, and tragedy to Elves and other peoples across Middle-earth.
The Silmarils are not the same as the Arkenstone in The Hobbit. The Arkenstone is a special jewel connected with the Dwarves of Erebor, whereas the Silmarils belong to the much earlier mythology of Valinor and the First Age.