The mercury content found in fish is from environmental exposure. It's a cumulative bio-toxin, meaning that as they ingest mercury it never really gets excreted out much, but continues to build up. It's generally not an issue except for relatively top end predatory fish. The prey fish on the low end of the chain get very low exposure, but the predators above them get exposed to the whatever their prey was exposed to. So that predator, which might be 2-10x the size of the prey, gets the same exposure as the cumulative amount as the hundreds or thousands of prey fish it eats saw. And the next one up the chain, and so on, until a human catches it and eats it.
For fish you are raising that is not much of an issue. In that case the only way to keep them from building up mercury would be to ensure that their food was free of mercury (no idea how you do that). But they can also get some exposure from dust borne mercury. Nothing much you can really do about that, other than keeping the fish in a closed system that prevents outside dust from getting in. Which would be very difficult and costly.
Best bet is to cut the fish to minimize the amount of mercury you ingest from them. Most of the mercury will be found in the belly fat. So if you trim that away you eliminate the largest source of possible mercury contamination. Sorry - that's PCB's that are in the fat. Mercury is in the muscle.
I looked into how mercury gets into fish in the ocean, and it says the water gets contaminated by industrial spilloff as the main way, so testing whatever water source you're using would be a good first step, but if you're using well water or rain water you can be pretty certain there is no excess mercury. Secondly, mercury gets concentrated the higher up in the food chain you go so herbivorous fish would have less mercury than carnivorous ones, but this only applies if the prey items are loaded with mercury. If you are, for example, feeding the fish earthworms from your garden, odds are good there wouldn't be much mercury in it. if you are sourcing the prey from the ocean, then there might be a worry.
Ah, just saw something where mercury in the air will 'settle out' into lakes or ponds, so maybe a well-fed pond is still a risk... Well, maybe the first step then should be to contact your local Fish and wildlife people to see if there are any mercury concerns in local waters.
My studies in the matter agree with those above. Most of my fish comes from a river. Mostly asian carp is what I get now. They only eat microscopic stuff, so are just number two on the food chain. The meat, sans fat, has an amazingly clean taste no matter the size of the fish. Other fish will often have a certain size limit before the meat starts developing a bad taste. Particularly predatory fish, and especially scavengers. I can't stand catfish from the rivers/lakes here, but I can tolerate them from ponds.
I would say harvesting them young could help prevent contaminations, and maybe growing plants that naturally clean the ground or water and could be harvested to remove toxins could help? I doubt the average pond would have issues with mercury, though.
And he said, "I want to live as an honest man, to get all I deserve, and to give all I can, and to love a young woman whom I don't understand. Your Highness, your ways are very strange."
Selenium. Selenium will inhibit the uptake of mercury as it is more readily absorbed. It basically takes the place of whatever the mercury molecule would be absorbed/form a complex.
How do I know this? Well selenium pollution is a huge issues in our local rivers due to upstream mining activity. A little selenium is fine, if not beneficial, however high levels become toxic to fish and other aquatic wildlife. Our area is also known as a fly fishing destination and the fish population is closely monitored. Turns out our fish a low in mercury because of the high selenium levels.
So I can't say what levels are healthy for fish but there is a potential to use selenium to inhibit mercury uptake. Selenium is an essential micronutrient and is involved in cell repair and is an antioxidant. Again, good in small doses.