No. Issue creation is a project level permission, not issue level.
There are some hacks and workarounds (like using validators that the user in the wrong group can never fulfil), and you might want a look at the Behaviours plugin as that can get you quite close.
...be more productive while being fun to use at the same time. For some, getting started can be a bit intimidating. This is especially true if Jira Service Desk is your first exposure to Atlassian...
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