Aquaponics work means the use of wastewater resulting from fish culture, for growing plants (any plant ... lettuce, onions, herbs, tomatoes ... even potatoes). Water from aquaculture is charged with nutrients. You can use any fish species. It must nevertheless assessed the metabolic rate in different species of fish, to be in accordance with the biological requirements of the plants. And must taken into account the fish density, fish size, temperature, etc. Aquaponics cultures can be implemented even in the mountain areas, where it's cold. You have in attachment some images from mountain area, where the waste water is used for growth of plants. 

Here is a link to software we've recently released which allows you to evaluate the economics of your aquaponic system configuration.

http://www.ctsa.org/index.php/news/download_free_aquaponics_decision_software

Any fish that can live in temperature needed to grow the plants is suitable for aquaponics. Even crawfish, yabbies, and shrimps are raised in aquaponics system. But you may want to look at growth rate, adult size and temperament etc to choose the best for your system (no system is created same in terms of size, design and type)

Source: https://www.leaffin.com/aquaponic-fish/

Other animals like turtle and duck also produce waste that can be absorbed by plants, hence are used in aquaponics.

I recently learned about Microponics that integrates micro-livestock with aquaponics along with fish, plants in a semi-controlled environment. The symbiotic relationship is the binding force/block of aquaponics. You can give bees farming and lady bugs the place in this chain for pollination and pests control.