Bones of fishes (Osteichthyes) are rich in Ca and P, which increases the strength and density of bones and teeth. However the process of cooking often changes the parameters(see attachment)
I think you have to add a few details, so that your question is in the right context (which countries do you have in mind e.g.) .
Here in Germany we eat fish (and shellfish) year round. But there is a saying, that you should not eat mussels in months without "r", that is June-July-August, which is exactly summer ! The reason is, that during this time the probabilty that large (potentially toxic) phytoplankton blooms develop, is much higher. And then mussels would be toxic too.
I agree with all the previous answers. I would like to add that some species are better from an organoleptic point of view in a given season while other species are better in another season. This fact is connected with the reproduction of species and perhaps also with the diet of the various species. I would also like to mention a proverb that says: "Eat short fish in long day and long fish in short day". It means that during the winter the long fish, such as eels, morays, etc., they are organoleptically better than they are in the summer, while during the summer the short fish are tastier than they are in winter.
Yes, I agree with you. Fish consumption decreases in hot seasons. However, this does not indicate that the fish is unhealthy food during the hot season. It is healthy food whenever it is eaten. However, whenever it is eaten, it is necessary to pay particular attention to nutritional health. I think there are two reasons for consuming less during hot times. Firstly, the warm season is a breeding period for many species of fish and there is a prohibition of hunting. It is also the period of growth of fish (eg for carp) in aquaculture. So, it is a bit problematic to find fish for fresh consumption. The second, it stems from the food culture and habits of societies. Seasonal eating habits can be seen according to regions. But, the fish cooked on the grill especially in summer is ideal for me.