The Doctor's wedding ring

The Twelfth Doctor wore a gold, dual banded wedding ring with a green stone in honour of his marriage to River Song. (PROSE: Twice Upon a Time)

When he regenerated into the Thirteenth Doctor, the ring was too big for her finger and fell off her hand. (TV: Twice Upon a Time)

Behind the scenes
"This timeless gold ring contains green amber collected by the Doctor on the planet Raxacoricofallapatorius. It reminds him of all the wars he has won but also all the lives he has taken. This thought lurks on his conscience to this day. To Peter, Best wishes being the New Doctor Who from Idris (11)"
 * One of the ring's two bands was Peter Capaldi's own wedding ring, which he preferred not to remove during filming. The band with the green stone backed up against Capaldi's own ring and was made by Rowley's jewellers in Penarth. The presentation box included a note to Capaldi regarding the ring's origins, written by the jeweller's son. This origin was later referenced in promotional material for Doctor Who Experience.

- Idris (11)

In the final scenes of TV: Twice Upon a Time, when the ring fell off the Thirteenth Doctor's finger, Jodie Whittaker was only wearing the secondary band for the shot.