apple ID not working for app store and itunes

I formatted my mac today and while reinstalling it took the oldest OS (OS X). When installed I didn't sign in with apple ID thinking I will do it post installation. However, when the mac was ready to use I can sign in to iCloud but not to App Store or iTunes.

It says, An Apple ID verification code is required to sign in. Type your password followed by the verification code shown on your other devices. I have allowed and password is there for me ready, but the login screen which says this remains as is and doesn't go the next screen for me to enter the password.

When I click login again, it takes me to "forgot password" screen. Its bit weird.

Also, when I tried to create a support ticket, I could see my other apple laptop, phone and watch but not the laptop which I reinstalled.

Any help?