Fjola's Wedding Band is obtained during a miscellaneous quest given by Christer inside Mistwatch. If the Dragonborn chooses to get rid of Christer for Fjola, she'll present them with this gift. It is also possible to kill her to obtain the ring.
If the Dragonborn tells Christer that Fjola is dead, he will tell the Dragonborn to keep the ring.
When the Dragonborn approaches the Mistwatch fort there are approximately four bandits of varying difficulty named Mistwatch Bandit. Upon entering the fort, walk up the steps on the left side to reach the drawbridge and pull the lever to lower the bridge, walk over and enter the North Tower.