What is this piece of fatty thing, inside a fish (a large snapper) which was near the roe? I had a quite large female snapper, it had large amount of fish roe, but nearby it was an interesting piece looking like pure piece of fat, quite hard and solid.
Here is a photo, these are the two large white things taking up most of the photo. The reddish thing in the upper-right corner is from a different fish, but I suspect its fundamentally the same kind of thing.

What is this organ called and how do you eat it?
Those look like the ovaries.
I don't know how anyone else cooks them, but I usually prepare them with a simple Japanese recipe: simmer in a water, dashi, sake, mirin, sugar, soy sauce, ginger mix. Great companion for drinking!
A quick search and I can't find any recipes for this in English... You could search &quot;真子&quot; and &quot;レシピ&quot; to find other recipes (in Japanese). There's a few videos on Youtube as well.
(Remember to remove the fibers and membrane and remove the blood gently, then wash with cold water/run it through hot water/lightly salt to remove the smell.)