Query agent jobs for a given notification operator name
Please try following T-SQL query:
 USE [msdb]
GO

   SELECT j.[name] AS [JobName]
    FROM [dbo].[sysjobs] j
    LEFT JOIN [dbo].[sysoperators] o ON (j.[notify_email_operator_id] =o.[id] )
    WHERE o.[id]=1 ----or o.[name]='your operator name'
     and j.[enabled] = 1 
        AND j.[notify_level_email] IN (1,2)

This should be able to query the jobs for success or failure notification to a specified operator.