1)"My brother mentioned reading about it in a newspaper."

OR

2)"My brother mentioned having read about it in a newspaper."

OR

3)"My brother mentioned his reading about it in a newspaper."

OR

4)"My brother mentioned his having read about it in a newspaper."

I would use 1) in conversation or just when it's not necessary to emphasize whether he's been through reading an article in the news paper or just read some paragraphs.

I would use 2) when it's necessary to emphasize that he's been through reading an article, whereas 3) and 4) seem weird to me in terms of "his".

I seek advice from educationalists.