Which is the most appropriate/correct usage?
- Are you angry on me?
- Are you angry with me?
- Are you angry at me?
Which is the most appropriate/correct usage?
- Are you angry on me?
- Are you angry with me?
- Are you angry at me?
I have never heard the phrase "angry on" used before.
Regarding the other two, I would say that it depends upon the context.
If directed at a person "angry with" should always be used.
e.g. I was very angry with her.
If directed at a situation I believe "angry at" would also be acceptable.
e.g. I was very angry at how rainy it was.
The key is who the anger is aimed at. "Angry at" is not really aimed at anyone.
So in the example you give, "Are you angry with me?" is correct.
Not sure how much use Google NGrams is here. It does at least show that "angry on" is used very rarely:

The second one:
Are you angry with me?
is correct. Curiously, we also say "are you mad at me?" which can cause some confusion.
Both angry at and angry with are correct. But 'angry on' is incorrect.
angry at/with somebody -
Are you angry with me? Are you angry at me?
References-
angry with (sometimes at) a person - Basic English Usage by Michael Swan
https://dictionary.cambridge.org/dictionary/english/angry -
He's really angry at/with me
https://www.oxfordlearnersdictionaries.com/definition/american_english/angry
Please don't be angry with me.
https://www.ldoceonline.com/dictionary/angry -
My parents were very angry with me.
You can say that someone is angry at someone
Please don’t get angry at me.
https://www.youtube.com/watch?v=GTEailc5QSI -
Don't get angry with him. (Don't get angry at him)