Both of your suggestions are correct and easily understood. Perhaps it is rather British English and a bit old fashioned, but ending a sentence with a preposition is a little clumsy, so you might write:
"This is the river in which to fish."
Although it would sound a little formal if spoken.
I don't quite follow your first meaning 'Is it the river of the fish?'
It is quite usual in the UK (particularly for those involved) to use the verb to fish without a preposition, for example, 'Which waters does he fish?' So both of Akasaka's sentences could mean the same thing here.
I'm trying to match the linguistic aspects of the Japanese language to decently communicate with the original thread creator who uses Japanese. Understanding an audience and knowing how to communicate is an aspect of effective communication.
However, there is probably a better way to word what I have worded. To answer your question, however, I will say this:
a) Is it the fish's river?
b) Is it a river for fishing?