All living organisms have nucleic acids that determines their physical characteristics and is passed on from parent to progeny when they reproduce.
In organisms like fish and mammals the genetic profile is determined by DNA which consists of two very long strands of nucleotides that are twisted to form a double helix.
DNA is made of 4 base nucleic acids known as adenine (A), cytosine (C), guanine (G) and thymine (T). The DNA of fish and that of humans is made up of these four bases.
But that is where the similarity ends. The number of genes that each of the organisms has differs. As humans are more complex organisms than fish, the number of genes is higher. Also, the physical characteristics of humans is different from fish in many ways, for example humans cannot live under water and fish cannot live out of water, humans produce live offspring while fish produce eggs, etc. For each of these differences separate genes are present in each of the species.
This is how the DNA of fishes and humans differs, not due to a difference in the base structures but by the difference in the number of base structures and how they are arranged.