This is a photograph of him and his brother.
This is a photograph of he and his brother.
This is a photograph of his and his brother.
Which pronoun is suitable, "subject pronoun","possessive pronoun" or "object pronoun" in this sentence?
The second sentence is ungrammatical since He is not the subject.
The first sentence is correct. You use it if you want to express that he is the subject of the photograph, which means that the photograph shows him.
The third sentence shows possession. It means that he owns the photograph. The photograph may not show him but the photograph is his.
The first and the third sentences are grammatical and idiomatic, whereas the second isn't correct.
If you are talking about their image, you use the first sentence.
On the other hand, if you are talking about the possession of the photograph, you use the third sentence.