Despite its faintness, the constellation Capricornus has one of the oldest mythological associations, having been consistently represented as a hybrid of a goat and a fish since the Middle Bronze Age, when the Babylonians used "The Goat-Fish" as a symbol of their god Ea.

According to some ancient Greek myths, it started with the sea-goat Pricus. He was the father of the race of sea-goats (half goats half fish), who were intelligent and honorable creatures. They lived in the sea near the shore. They could speak and think according to Greek legend. They were favored by the gods.

Pricus is tied to Chronos, the god of time in Greek myths. Chronos created the immortal Pricus, who shares Chronos's ability to manipulate time. He had lots of children who lived near the seashore, but when they found themselves on the dry land they turned into normal goats, losing their special ability to think and speak in the process. In an effort to prevent this, Pricus turns back time, again and again; however, he eventually resigns himself to loneliness and misery, letting the little Sea Goats leave him.

Learning he cannot control their fate and not wanting to be the only Sea Goat prompts him to ask Chronos to let him die. Because he is immortal instead, he must spend eternity in the sky as Capricorn.

More Info: en.wikipedia.org