I need to cancel my LinkedIn premium subscription and wanted to have refund against what was deducted today in the morning

To stop a subscription follow the steps in this guide:

See or cancel your subscriptions - Apple Support

When the subscription shows Expires on [Date]

That means the subscription is canceled.

If you are still unable to cancel the subscription:

Contact Apple for support and service - Apple Support

You can request a refund by following the steps in this guide:

Request a refund for apps or content that you bought from Apple - Apple Support

You are not guaranteed a refund tough.

This is an automated process, if you wish to explain your situation in-depth to a person you can:

Contact Apple for support and service - Apple Support

Also, see this:

How long refunds from the App Store or other Apple services take - Apple Support

Good luck!