You can’t “add” a file to a deploy; they are immutable. But perhaps we can help you find a different solution that helps you meet your needs!
The usual way to get auth into Netlify but not in git, is to use environment variables during build - you set them in our UI (on the deploy settings page, scroll down to environment variables), and interpolate them during build.
If that won’t work for you, let me know some more about why and I’ll try to come up with a different solution for you.