When configuring the 'SQL Agent - Jobs Failed', you can't modify it under one connection.
By design, the action setting is effective for an alarm for default settings (all connections) or an alarm for each connection for which you have created special rules.
So, you cannot define an action to a severity separately from other severities.
In this particular scenario:
1. Open Alarms dialog
2. Select the connection you want to configure
3. Select “SQL Agent - Jobs Failed”
4. Check “Override the default settings…”
5. Change Severity from “High” to any lower level. (This is for Default Severity)
6. Click “Add…” button and select a job you want to configure
7. Set severity for this job high
8. Check “Send an email…” and configure email settings.
9. Make sure “when the severity is…” is set to “High”
In this scenario, other jobs will be alarmed in lower severity (for this connection only)
Alternatively, if number of jobs are just a few,
just enable and configure email settings and filter out other jobs by using “Do not alarm for certain values”
In this case, other jobs won’t be alarmed any more (again, for this connection only).