Notifications from Apple on MacBook air So, I tried to install newly purchased iPhone 5 and after logging into my apple ID account, a pop up message notified me that a verification code has been sent to macOS Sierra, where can I access the code on my laptop?
Furthermore I cannot now even verify the account because it is impermanently blocked as I tried too many times to enter a password for my Apple ID. Now I remembered it btw. So, to reset the apple ID password they ask me to enter a password for my macbook AIR, I am very sure of the password because I use the laptop every day, but when I enter the MacBook password the pop up message gives me an error and notes, that the entered password is incorrect. Do I even understand correctly that I need to enter the password which I enter when try to log into my computer, is there any other password am not aware of? 

Now I manage to log into the phone and install different apple ID, but I have a problem to reactivate the old apple ID on my mac and also the phone, because on both devices they ask to verify the code sent to the other device, which I cannot access.
I've had multiple Mac computers and iOS devices and when I get a new device I get a pop up similar to what you mention (it just appears on the screen, as shown in the image below -- so I don't have to "do" anything). I have 2-factor authentication enabled, and you may check if you do as well. This site has more details.


You write that you are asked to "enter a password for my macbook AIR". That may be true, but also be careful to distinguish between the verification code they send and your MacBook Air login -- two very different things, and if you confuse one for the other I could imagine the frustration.

You may also find this page helpful as it specifically deals with Apple ID sign-in on different types of devices and (at the very bottom of the page) gives links to help in the situation you describe regarding forgetting your Apple ID.