You’re yelling at your daughter to clean her room. She says, under her breath, “I hate you!’. Now you’re extremely angry, and you can’t believe she said that. You say:
What did you just say to me?
One of the uses of "just" is to express that something happened very recently. It can mean a few minutes before:
I'm sorry, he just walked out to go get lunch.
Or immediately before:
What did he just say?
Or it can mean a few years:
Mankind has just started to study ways to understand and control DNA.
But in any case, "just" means a short time before.
If you didn't hear what someone said, you can ask:
What was that?
What did you say?
But asking "What did you say to me?" has a completely different meaning. You say this when someone insults you, challenges you, or says something rude:
A: Shut up.
B: Excuse me? What did you just say to me?
You should say this in an angry tone of voice, and stress the word "what".
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