Cannot login to Mac App Store with Apple ID, it always tells me to reset password

Hi!

I cannot login into the Mac App Store anymore with my Mid-2012 MacBook Air running OS X 10.10.5 (Yosemite).

When trying to download anything, it asks for my Apple ID credentials. After entering them and going through the Two Factor Authentication, I get the message that my password has been entered incorrectly too many times (which I did not) and it has to be reset. After following the instructions to reset the password, the Mac App Store continues to show me this error message. I can use my Apple ID on my iPad mini 4 without any problems, before and after resetting the password.

What can I do to resolve this issue? I am unable to upgrade to El Capitan or get/update any Apps.

Thanks for your help!