I'm new to iOS App Development. Is it possible to show only the Mail apps which was installed in iPhone in the UIActivityController.
Not exactly. There's no way to specify the kind of apps you want to show in there. However, there is a way using which you can specify the type of services you wish to exclude.
UIActivityViewController has a property excludedActivityTypes. You can exclude all other types of activities except mail
You should be able to narrow the list of apps down quite a bit.