Leaving fish out in the freezer bag on the counter overnight is generally not recommended, as it allows the fish to enter the temperature danger zone (between 4°C/40°F and 60°C/140°F) where bacteria can multiply rapidly. Bacteria growth can lead to foodborne illnesses if consumed.
Putting the fish back in the refrigerator afterward may slow down bacterial growth, but it doesn't eliminate the potential risk entirely. The quality and safety of the fish depend on various factors, including the initial freshness of the fish, the temperature at which it was left out, and how long it remained at room temperature.
It is always best to err on the side of caution when it comes to perishable foods. If you have any doubts about the safety or quality of the fish, it's generally advisable to discard it to prevent the risk of foodborne illness. If you are unsure, it's a good idea to consult a local food safety authority or a healthcare professional for guidance specific to your situation.