Hippocampi

 They were the fish-tailed horses of the sea. They were depicted as composite creatures with the head and fore-parts of a horse and the serpentine-tail of a fish.

The ancients believed they were the adult-form of the small fish we call the “sea-horse”. Hippocampi were the mounts of Nereid nymphs and sea-gods, and Poseidon drove a chariot drawn by two or four of the creatures.

Hippocampus in a Roman mosaic in the thermae at Aquae Sulis (Bath).
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Hippocampus in a Roman mosaic from the House of Neptune, Italica.

Other fish-tailed land animals which appear in ancient art include the Leocampus (fish-tailed lion), Taurocampus (fish-tailed bull), Pardalocampus (fish-tailed leopard), and Aegaecampcs (fish-tailed goat). 

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Leocampus in a Roman mosaic from the Baths of Neptune, Ostia.
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Taurocampus and Aegaecampus in a Roman mosaic from the Baths of the Lighthouse, Ostia.