Thoroughly rinse the fish bones under cold running water, removing any traces of blood. Place the bones in a stockpot and cover with water. Bring the pot to a simmer over high heat, then strain out the bones and discard the water. Wash the pot before proceeding.

Return the fish bones to the pot, add the carrots, onion, and celery root, and cover with fresh water. Bring to a gentle simmer over high heat, skimming any foam or impurities that rise to the surface. Reduce the heat to medium-low and simmer for 45 minutes. Strain out the solids and discard them. Return the poaching liquid to the pot. Set aside.

Meanwhile, combine the fish, eggs, matzah meal, grated carrot and onion, salt, and pepper to taste in a food processor. Begin processing, gradually adding cold water 3 tablespoons at a time until the mixture becomes smooth and uniform. Continue processing and adding water as needed until the mixture is uniform and gelatinous. 

Return the poaching liquid to a medium-high heat, add the carrot coins and bring to a gentle boil. Season with salt and pepper to taste.

Using wet hands, form the fish mixture into oval patties, roughly ¼ cup each, and carefully slide them into the pot. Bring the liquid to a gentle boil, then reduce the heat to a very low simmer. Partially cover the pot and poach for about 30 minutes, until the gefilte fish is pale and the carrots are tender. Remove from the heat and let cool for 30-45 minutes.

Transfer the gefilte fish and carrots to a container and pour the poaching liquid over them to cover and refrigerate overnight. 

For serving, arrange the gefilte fish on a platter, placing one carrot ring on top of each patty. Serve cold or at room temperature with a side of chrain (prepared horseradish).