How to log in apple id on 10.10.5 Yosemite

When you attempt to sign in to your Apple ID on the 2009 iMac running Yosemite, is the six digit code being sent to your other devices?

I understand that code is not appearing on the iMac, but if you are receiving that code on the other devices try appending it to the password you are entering on the iMac.

In other words if your Apple ID password is My2FluffyKittens and the six digit code sent to your other devices is 123456, then type My2FluffyKittens123456 in the password field on the iMac.

Let's approach these concerns one at a time.

I understand you made an iTunes purchase but you are unable to download it on the Yosemite iMac. Can you view your iTunes Account using its Account menu > View My Account... ? It should prompt for your Apple ID password. If that does not happen, describe what happens instead.

Try Account > Sign Out and then try signing in again. Describe what happens.

• For example, on one very old Mac, I occasionally encounter a dialog alleging my iTunes session has expired, and it prompts me to sign in again. I provide the Apple ID credential only to encounter the exact same dialog again. Again and again. That may repeat six or eight times in succession, which is obviously annoying, but it eventually relents. Who knows why that happens but I have been purchasing iTunes content since its inception a couple decades ago. The annoyance only occurs on older Macs running older OS X versions and Apple stopped caring about them long ago.

System preferences >>> iCloud does not generate the code ...

I'm not sure it's supposed to, so it's not clear to me what you're expecting there.

All my devices new and old were working until Mail stopped working (for one of the three accounts in Mail) and this random request to log into my AppleID was requested.

If you are not receiving email messages from one particular account, the gold standard for fixing that is to delete the problematic email account(s) and add them again. Refer to If you can’t send or receive email on Mac - Apple Support, under Remove your email account, then add it back. If you determine you are unable to add that account again, it is likely the particular email account server will no longer function under Yosemite. For example, I happen to know it is no longer possible to add "newer" Microsoft Exchange server hosted email accounts to "older" OS X versions of Mail. One day they simply stopped working. The same may be true of other email services. We're just out of luck in that case.

The oldest macOS version I have at my disposal is El Capitan so I am unable to replicate that problem exactly, but View My Account is working as it should. The iTunes Account on that Mac does not show any available downloads, and I don't know how to force a download to occur.

The only suggestion I have would be to sign out of that account on that Mac, and sign in again. You might also try "deauthorizing" that Mac and re-authorizing it again.

Don't "deauthorize all" unless you are prepared to wait a year before you can do that again.

That's all I can come up with.

As long as you're getting the six digit code on your iPhone (or other eligible device) that's all Apple needs for you to log into a device — any device — with that Apple ID. My only unresolved question is why it's not working for logging in to iCloud to receive email.

I may be misunderstanding the problem. How does this page (Apple Support Communities) relate to using System Preferences > iCloud? Is there one specific service for which that Apple ID and password is not working? Unfortunately I don't recall if there is anything unusual about Yosemite. The oldest macOS version I have to work with at the moment is El Capitan. It receives the two-factor codes the same as any newer Mac.

I do understand the distinction between two-step and two-factor. As I recall once you start using two-factor we can't go back to using the older method, but I do recall having to append the six digit code to the password the way I described for older OS versions. Whether that applies to Yosemite or not I don't recall.

Use two-factor authentication - Apple Support