What I can think of is turn off this notification option "Notify all users on new post" from backend, you can refer on my attached screenshot below.

So when the new discussion created on your site, it will not notify to all of your site member, it will only notify to admin and subscriber on your site.

And then for those your site user if want to get new discussion post email notification, they have to subscribe on your forums single category page.

The solution you describe is to stop sending notices of new discussions to those who have not subscribed. This is not a solution. What I am asking is a way to either select a Joomla group who will be notified of all new discussions or to exclude a Joomla group from all discussions. Right now, Joomla groups who are not able to do anything in easydiscuss also get the email of new discussions when the notification email is turned on.

Hello Michael,

It is not possible to only notify a specific group of users in EasyDiscuss currently. In EasyDiscuss, you could either notify everyone or notify only people who subscribed.