By Prince Sidon's palace there is a secret shrine. After beating the divine beast, a girl sings a song about a ceremony. I learned that the man hosting the ceremony dropped the weapon into the river by the palace. I went in the water and used Magnesis to try and find the weapon to no avail.
Does anyone have an idea where the weapon is at or where they found it?
The Ceremonial Trident is located underwater right by the northwest bridge, near where Trello tells you he dropped it in the lake. This video shows the location exactly.
Once you've found it, you can use a combination of Cryosis and Magnesis to fish the spear out of the water.
In addition to the ceremonial version of the weapon, that's location is discussed in MageXy's answer. You can also use the Lightscale Trident that you receive for completing divine beast vah Ruta to open the secret shrine.
