There is a requirement to transfer the Search Index role to another server on the farm in order to reduce the load on a particular server. So went to “Central Administration > Operations > Services on Server”
I wondered, “Office SharePoint Server Search” is missing in Servers on the Server!!!
This is because: When you install SharePoint, You have to choose “Complete” installation instead of “Web Front End”.
Unfortunately, There is no way to fix this other than: uninstall and Re-Install SharePoint on that particular machine.
So be careful which option you’re choosing, because after a wrong decision, I had to suffer here.