Oil spills pose a grave threat to fish as the oil is very sticky and it clogs the gills of fish preventing them from taking oxygen dissolved in the water.
The process of photosynthesis is also affected by oil spills but this has nothing to do with fish dying due to the oil clogging their gills. Marine plants and other organisms that are able to produce oxygen as a result of photosynthesis require sunlight as a source of energy. Photosynthesis is an endothermic reaction and an energy source is essential for it to take place. The oil spill blocks sunlight from entering the water. It is an opaque coating floating on the surface and no light can enter the water below the oil.
As a result of the lack of sunlight plants cannot proceed with photosynthesis.