Cannot log in to iCloud on macOS Yosemite

I have set up on older MacBook Pro 2010 with a clean install of Yosemite 10.10.5. The whole purpose of this setup is to be able to access older software and older client files. This mac will NOT and CANNOT be updated to a newer OS for this reason. It needs to stay right where I have it.

That being said, I cannot login to iCloud. The username and password are correct, but it won't let me in. I do not want to change the password as I am using many newer devices and I know for a fact that changing the password across all devices will not solve this problem. It seems like it's an issue with this older macOS.

Any suggestions or solutions?