But fish is still brain food, right?

"It's not that eating fish is unhealthy per se, but there are issues that need to be considered before parents go overboard feeding fish to their kids to make them smarter and sleep better," said Samantha Heller, a senior clinical nutritionist at New York University Medical Center in New York City. She was not involved with the study.

Fish is a good source of lean protein and is high in omega-3 essential fatty acids, she said. These acids are highly concentrated in the brain and play important roles in neurological function. 

They are essential for brain, eye and neurological development in fetuses. They are also necessary for eye, heart and brain health in adults and may reduce systemic inflammation, Heller said.

"The concern with eating fish is not only the overfishing of our seas, but the amount of mercury —a neurotoxin —found in fish," she said.