The simple answer is it depends. Being able to refreeze your fish depends on how you thawed it out in the first place.
Refreezing Fish That was Thawed in the Refridgerator
It is safe to refreeze fish that was thawed out in the fridge. As long as the fish has maintained a fridge-like temperature where it has been cold to the touch, meaning at no point the fish had gotten warm enough to develop bacteria.
Refreezing Partially Thawed Items
You are able to refreeze items that have been partially thawed. Say you are wanting to cook half the bag of scallops you just bought but don’t know if you can refreeze them? All you have to do is partially thaw them in the fridge and then seal the unused portion in a freezer-safe bag.
What NOT To Do
If you quick-thaw seafood in the sink, it should NOT be put back into the freezer. The reason for this is that once fish is brought to room temperature, it then allows for bacteria growth.
When Refreezing Fish…
Make sure to refreeze your fish as soon as possible, since each day can diminish the freshness.