Currently Jira notification includes most of the fields of view screen. However, can we modify Jira notification mail for few fields only for one project?
If you were in a Standalone, you could customize the mail template vm files at $JIRA_INSTALL/atlassian-jira/WEB-INF/classes/templates/email directory. You would find vm files for each event in JIRA and one folder for text emails and another folder for html emails. However, I believe that there is no way to apply this changes for only one project.
You can find more information at Customizing Email Content page.
And also, these plugins below may help you achieving this:
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