Hi Is there any API or function by using which we can fetch the list of unsubscribers from the particualar Contact lists?
Unfortunately it's not possible to collect this information directly, as the action of unsubscribing automatically removes all list memberships for that contact. One possible workaround is that it would be possible to collect that information indirectly through campaign tracking data if the campaign was sent to a single list of contacts. You could accomplish this by viewing the opt out activity report for the email campaign, and referencing the sent_to_contact_lists for the campaign that was sent. You can find documentation for this reporting here: http://developer.constantcontact.com/docs/campaign-tracking/opt-out-activities-collection.html
If I can provide any additional information or answer any questions, please let me know!