A specific user is assigned to a test case.
When he tries to create an execution, he gets the error message "The logged in User is not the test case assignee". It will not create the execution.
This functionality isn't available natively in Jira. You can't get that granular in the notifications.
You might be able to do this with an add-on, Jira Suite Utilities or ScriptRunner for Jira. They maybe able to help you out, by setting a customized post-function on the workflow transition. but I have not tested them as a solution to your problem.
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