Contact Unsubscribe API method issue

Folks,

I am using Contact Unsubscribe API method but i am getting following error, It start happening now before it was fine.
It seems there is some issue on API end.

Contact Email zhafeez@wealthx.com
API response
{
    "message": "Subscriber does not exist. ",
    "status": "error",
    "code": "2103",
    "uri": "/api/json/listunsubscribe",
    "version": "1"
}

Is there any way or possibility, If we want to use http://zc1.maillist-manage.com/ for managing newsletter subscription for our users.
Can we have specific profile related urls, Our user will click the url and they can manager there subscription by them selft.

Regards,
Zulqarnain Hafeez