Possible the Monitor's EDID is not being read correctly by AMD Driver.
Try using Custom Resolution Utility and see if you can add 240Hz Custom Resolution. You can download it from here: https://www.monitortests.com/forum/Thread-Custom-Resolution-Utility-CRU
Also do you have Freesync enabled? If it is enabled try disabling to see if it fixes your issue.
What is the Make & Model of your Monitor's cable that you are using?