Thanks for the reply. Let me give you some more details.

We have the maintenanace plan created around 3 yr ago with SQL 2005. We migrated to 2008 R2 almost 1 yr ago. Everything is working fine till now.

In that backup which is running that maintenance plan has additional step which will send us custom notification about the job failure. Almost from last 10 days, we noticied the for the same scheduled the maintenance plan is running twice and we are getting 2 backups. So we disabled that job and created new maintenance plan for the backup but still it is running twice.

So we deleted both of the backup maintenance plans. After deleting that maintenance plans & backups jobs, we are receiving the job failure alert, which is added as additional step in old job.

I am sure, the alert is coming from the same instance because in the alert we will receive the instance name and the job name where it failed.