Hi Jyoti,
Yes you need to either be a member of the card, or watch the card (or the list or the entire board!). Once you opt in to notifications, those will come through as you expect: https://help.trello.com/article/793-receiving-trello-notifications
You might have a look at this:
https://community.atlassian.com/t5/Trello-questions/Deadline-reminding/qaq-p/914670#M8745
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