Fish Gods
Fish, fish-shaped beings and deities associated with water occur in different religious traditions. These categories overlap, but they are not identical. A sea god need not be a fish god, and the use of a fish as a symbol does not establish that one religion inherited the worship of another deity.
Andrew T. Austin discusses these themes in The Historia Illius Itineris. The examples below provide historical reference points for comparing images while keeping the traditions distinct.
Hatmehyt
The Egyptian goddess Hatmehyt is associated with Mendes in the Nile Delta. A fish appears on her crown and down her back in surviving representations. This differs from describing her as a mermaid. The Metropolitan Museum's record of a fish on a standard explains its local association with the goddess. Met collection record 89.2.610.
Matsya
Matsya is Vishnu's fish avatar. Representations can combine a human upper body with a fish form. The image belongs to Hindu accounts of divine manifestation and should not be assimilated to every other water deity simply because a fish appears. Met collection: Matsya Avatara (Vishnu's Fish Avatar).
Oannes and the apkallu
Oannes belongs to the tradition of Mesopotamian sages. A fish-cloaked figure is not necessarily a god depicted with a fish body: the cloak is itself part of the representation. Stephanie Dalley's study of the apkallu relates the fish-cloaked type to Berossos's description of Oannes. Dalley, "Apkallu", Iconography of Deities and Demons in the Ancient Near East.
Surviving objects provide a firmer basis for discussing the image than an unsourced claim about a particular temple or ritual. British Museum, fish-cloaked apkallu figurine.
Dagan and Dagon
Dagan, also called Dagon in biblical contexts, should not simply be identified as a fish god. The academic Ancient Mesopotamian Gods and Goddesses project describes the fish interpretation as erroneous. His precise functions and the derivation of his name require more caution than a simple fish or grain etymology allows. AMGG, "Dagan".
The accompanying illustration can be read as a later imaginative representation; it is not evidence that ancient worshippers represented the deity in that form.
Atargatis and Derceto
Ancient accounts associate the Syrian goddess with sacred fish and water. However, the forms and places must be distinguished. On the Syrian Goddess, attributed to Lucian, contrasts a partly fish-shaped Derceto with the fully human female image at Hierapolis. This makes a single universal "mermaid goddess" description misleading. The Syrian Goddess, sections 14 and 31, translation by H. A. Strong, with notes by John Garstang (1913).
Poseidon
Poseidon is a Greek god associated with the sea, rather than a deity normally represented as a fish. In Odyssey 9, Odysseus and his companions blind the Cyclops Polyphemus, who calls on his father Poseidon to punish Odysseus. The direction of the injury matters to the subsequent voyage. Homer, Odyssey, book 9, Samuel Butler translation.
Christian fish symbolism
Early Christian fish imagery has its own textual explanations. In On Baptism, chapter 1, Tertullian compares Christians to fish in relation to water and Christ. The Greek word for fish, ichthys, is also explained through the initial letters of a phrase naming Jesus Christ, God's Son and Saviour. Tertullian, On Baptism, chapter 1 and the translation's note.
This is evidence for a Christian use of the image. It does not demonstrate a continuous practice of worshipping earlier fish deities.