It's the Support Staff permission. It used to be called Manager but it was confusing since Joomla 3.0 (or 2.5? I can't remember — it was about a decade ago) when Joomla added permissions with the word “manage” in them at which point it became Support Staff. The two terms have been used interchangeably in the documentation and language files, mostly because we used to have official translations. Long story...
To make users in a user group become support managers (i.e. members of the support staff) for the entire component and all categories go to Components, Akeeba Ticket System, Options, Permissions tab and set the Support Staff permissions to Allow for that user group.
To do that for specific categories only go to Components, Akeeba Ticket System, Categories, choose the category you are interested in, Permissions tab and set the Support Staff permissions to Allow for that user group.
Remember that Joomla works with two inheritance levels:
1. a category's permissions override the parent category's permissions (repeat if there are more parent categories) which override the component's permissions.
2. a user group's permissions override the permissions of its parent user group (repeat if there are more parent user groups) which override the permissions set for Public.
Also remember that Deny always wins. If within any inheritance dimension there's a Deny for a permission that permission will always be denied — even if you try to allow it again. For an overridable deny use Inherit instead.
You may want to use the third party component ACL Manager to figure out which permissions apply for each user and why. Otherwise it's a loot like trying to solve a three–dimensional puzzle.
Nicholas K. Dionysopoulos
Lead Developer and Director
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