The "Sea Mosquito" was tested in March 1944 with carrier deck landing trials on HMS Indefatigable in the Irish Sea. The pilot (almost inevitably) was the legendary Eric 'Winkle' Brown.
He discussed the trials in a 2015 video, where he noted several problems with using the Mosquito in carrier operation, not the least of which was that the carrier’s arrester-gear limited the Mosquito’s landing speed to a maximum 83 mph, in an aircraft with a published stall speed of 110 mph!
The Sea Mosquito development and history is discussed in Michael John Hardt's book De Havilland Mosquito, from page 115. This includes details of the modifications required for the aircraft to be deployed from carriers (reinforced fuselage, A-frame arrester hook, Rolls Royce Merlin 25 engines with larger 4-blade propellers, and (from the 2nd prototype) folding wings).
In the event, they were never deployed operationally as the war ended before the planned mission (Operation Highball) could be carried out.