What is the story of Chhath Puja?

The festival has several intertwined legends -

• Legend of King Priyavrata: The story goes that King Priyavrata (son of Manu) and his queen Malini were childless. They performed a yajna (sacrifice) but still had a stillborn child. Then the Goddess appeared as Chhathi Maiya and revived the child, saying she protects children and blesses parents. From that time, worship of Chhathi Maiya began.
• Legend of Karna: Karna, the son of Surya and Kunti (from Mahābhārata) is said to have stood in water and offered arghya to the Sun God every day with devotion. His story is echoed in the rituals of Chhath — standing in water, offering to Surya.
• Legend of Draupadi and the Pandavas: During exile the Pandavas and Draupadi are said to have performed sun-worship (and Chhath-like rituals) on the advice of sage Dhaumya. Their fast and devotion helped them regain honour and kingdom.
  ThePrint
• Legend of Sita: In another version, Sita from the Ramāyana, after return to Ayodhya, observed fasts and offered devotion to Surya and Chhathi Maiya and thus the festival is linked to her too.

Because this festival is very old (with Vedic roots) and local traditions picked up different myths. For example, Chhath is linked to Surya worship in the Rig-Veda and downstream epics.