Hi Shubhendra, do you actually see it in the 'Add method' drop down or do you just see it in the list of Enrolment methods?
We use external database enrolment, and it only shows up in the list of enrolment methods for courses where there are students enrolled using it.
IE: If you create a new course named 'test', it will not show 'external database' under enrolment methods, until you add the 'test' course and students that are supposed to be enrolled in it, in your external database.
It will show up in Moodle when the matching course and enrolled students are present in the external database (and a student that is supposed to be in it logs in or you run the enrolment sync script, /enrol/database/cli/sync.php). Otherwise you won't see it.