Various studies on Goldfish's memory shows that it can learn quickly and recall memories for more than one month.
The study of long-term memory in fishes published by 'How Fish Behave' website mentions that Dr. Tony J. Pitcher had trained some Goldfish in his lab to choose the tubes of one color over another to get the food. The fishes were fed normally in the absence of tubes for one year, and at the end of the year, the tubes were inserted, and the goldfish immediately selected the tube with the correct color.
A Goldfish experiment by the National Center for Biotechnology Information (NCBI) proved that the fish could identify the separate sensory stimuli in feeding time. Even the University of Melbourne reports that researchers trained many young goldfish by playing a certain sound during feeding time. These goldfish were then released into the ocean. About 6 months later, the researchers played the sound again over a loudspeaker, and many of the goldfish returned to where the sound was playing.
Hence, several studies state that a goldfish can clearly remember things for longer than a few minutes or more than a month.