[Grammar] I've just heard my mother mentioning them once...

[kingtrn]

I don't know what is the correct way to say something like:

I've just heard my mother mentioning them once that they are living in California.

=> I mean: my mother once mentioned about my uncles, she said that they live in California, and I somehow heard that. So when someone asks about my uncles, I will tell them the above sentence.

 

[Raymott]

"I heard my mother saying once that they were living in California." (If you heard it once in the past they might not still be living in California.)
"I remember my mother mentioning once that they lived in California."
"I've only heard my mother mention them once. She said they lived in California."
"My mother once mentioned my uncles. She said that they lived in California." (Since that's what you say you mean). Remember with reported speech that you can always backshift the tense (and should, in my opinion).