I have not done the purchase application How is the amount deducted from my account without my knowledge

Maybe it's Authorisation Holds to identify you, the money will be back within a few days.

Read here: About payment card authorization holds in the iTunes Store - Apple Support

No one here can do anything. We are all iTunes users just like you.

What was the amount?

Did you look at your purchase history to see what the charge was for?

Could it be an authorization hold?

Does threatening a law suit ever help you get anything accomplished. Perhaps skipping the threats and simply explaining your issue in far greater detail would be more effective.

How much was deducted ?

Is it a temporary store holding charge (see the link in ckuan's reply) ?

Or does the app have an auto-renewing subscription ? Just deleting an app does not cancel subscriptions, you have to cancel them : View, change, or cancel your subscriptions - Apple Support

We are fellow users, we don't know what has/hasn't happened on your account(s).

You didn't buy what application ? Where are you seeing the 'purchase', on your credit card, iTunes account's purchase history, (phishing) email receipt ?

If you've downloaded an app with an auto-renewing subscription (some VPN apps have subscriptions) in it then did you cancel the subscription ? Just deleting an app does not stop a subscription

Does it/they show on your iTunes account(s) purchase history : See your purchase history in the iTunes Store on a Mac or PC - Apple Support ?

If they do, and if nobody else has access to your account/computers/devices and did it, then change your password (http://appleid.apple.com ; What to do after you change your Apple ID email address or password - Apple Support), and contact iTunes Support (there is a 'contact us' link at the bottom right of every page on here)

If nothing shows on your iTunes account(s) contact your card issuer

Not entirely sure what the first half of your post means, and whether you have or haven't downloaded an app, whether it has an auto-renewing subscription in it, and if it did whether you didn't turn its auto-renewal off. But contact iTunes Support and see what they say and whether they will refund you

Auto-renewing subscriptions are automatic, you have to turn them off to not be charged. Contact iTunes Support and see what they say

Did you read the app's description page in the store, and if you did, what does it say ? Have you now unsubscribed to it ? Have you contacted iTunes Support in your country (and which is therefore the country on your account) ?

You already know that we are fellow users, these are user-to-user forums, nobody on here can potentially refund you - contact iTunes Support.