I can't sign in App Store and iTunes with my Apple ID

Are you getting the verification code so that you can sign in? See if this helps.

Apple ID - Get a verification code and sign in with two-factor authentication

If you see a password box, enter the password (ABC) followed by the code (123) or ABC123.

If you don’t see a password box, try selecting a different preference pane, and then go back to the iCloud pane to see if you get a password box.

It seems you might have two factor authentication. Did you get a code via text or on another device or computer?

https://support.apple.com/en-us/HT204974