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.