There are many alternatives to aquaponics fish farming. The principle remains the same, but these methods are still at the experimental stage. Nevertheless, many people are successfully using them on a small scale.
Any animal producing ammonia can be used.
Ducks are a good alternative to fish. They produce a large amount of nutrients that can be used by plants.
Ducks are easy to feed.
Secondary benefit: ducks produce eggs and ducks are good meat producers.
Freshwater shrimp can be a good alternative but you will need many details on how these animals are raised.
Turtles are another credible alternative to fish. Aquaponics with turtles remains very rare.
Vermiculture uses diluted leachate (worm tea) as a nutrient solution.
Crayfish are another credible alternative to fish. They feed mainly on plants and are therefore easy to feed.