Hi
Could you tell us if you are using any of the following please
JCommentsCommunity BuilderKomentoAlta User PointsAcymailing
As Arno said the function 'existsCustomFieldsTitles()' is not included in the jD3.9 series.
Because this is only affecting Download Details I believe it is probbly being caused by JComments or Komento as they use Download Details to show their comments.
There are details of how to upgrade those Components in the Third Party Extension section ofhttps://www.jdownloads.net/documentation-for-v3-9/getting-started-v3-9/upgrading-from-jdownloads-3-2-to-3-9
ColinPS would help if we could access the site please
There are also details in the section "Extending jDownloads with other extensions"
https://www.jdownloads.net/index.php?option=com_content&view=category&id=35