Hi there, kaushal33.
Congratulations on your new iPhone 12 mini!
It appears that you're having a problem with your iPhone 12 mini. You're finding it difficult to unlock your phone and the Home screen doesn't respond well either. Good job in discovering that removing the case resolves the issue, and we're glad to help with this.
About iOS 14 Updates - Apple Support -- There's been a recent update to iOS 14 that fixes issues involving the Lock screen of your iPhone 12 mini.
How to back up your iPhone, iPad, and iPod touch - Apple Support -- Before proceeding, please be sure to have a recent backup.
Update your iPhone, iPad, or iPod touch - Apple Support -- Update your iPhone to iOS 14.0.1 and see if your Lock screen and Home screen respond normally now.
If either screen still isn't responding, it's time for a new case made specifically for your iPhone 12 mini, and Apple has several to choose from: MagSafe - All Accessories - Apple
Cheers!