I've done a lot of searching on this, and I haven't found any hits with the same situation. macOS Mojave 10.14, Xcode 10.1, GitHub Enterprise 2.14.10.
I have an SSH key that is configured in GHE and works fine from several other places, including this very same Mac's shell and ssh agent, from the same local repo. i.e. remote operations fully work from the shell.
Further, I think they worked from Xcode in the past, but I'm not certain. It's also possible that I changed the key's passphrase since it last worked.
But when I select this key file from the Source Control operations, I get an error that:
Authentication failed because the credentials were rejected.
Verify the authentication credentials were entered correctly and try again.
I'm not being prompted for the passphrase (or any other credentials). It's as if Xcode is remembering some incorrect credentials, but still not asking me to re-enter after failure.
Xcode also earlier complained, when I first selected this file, that there wasn't a .pub file with the public key in the same directory. So I created that, using ssh-add -L to ensure I was copying the same public key as is loaded in my working shell and SSH agent.
I also tried copying the key files from their non-default location to ~/.ssh, and even tried renaming them to the default id_rsa name that Xcode first tries, but neither of those made a difference.
(What I haven't tried is creating a whole new key and uploading that to my GHE. I will if nothing else works.)
