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
The ring was made by Rowley's jewellers in Penarth. The son of the jeweller wrote a note to Peter Capaldi regarding the ring's origins, which was included in the presentation box.

"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)"

- Idris (11)

The ring was, in actuality, two bands, which comprised of Peter Capaldi's own wedding ring, and a separate band with the green stone, which backed up against Capaldi's own ring. This was done so Capaldi would not have to remove his ring during filming. 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.