The popular belief is that in the Aparajitha form, Mother Goddess vanquished all those that were practicing Adharma. She protected those following dharma.
In Hindu iconography, she is depicted as a formidable and powerful woman with three eyes. Her hair is intricately styled like a crown, adorned with the crescent moon. She possesses four arms, each holding a different symbol: the pinaka (Shiva's bow), an arrow, a sword, and a shield. Her wristlet is formed by the serpent Vasuki, and she is often portrayed riding a lion.
The Devi Mahatmya features a captivating hymn known as the 'Aparajita Stotram' (5.8-82). In this hymn, the Devas, led by Indra, sing praises to Devi to seek her favor in vanquishing the demons Shumbha and Nishumbha. It was a tradition in ancient times for kings to venerate her on Vijayadashami, securing their belief in assured victory in battle.
The form and attributes of Goddess Aparajita is mentioned in the Devi Purana and Chandi Patha.
The rituals and pujas associated with Aparajitha are mentioned in Tantric texts.
Some devotees observe a fast on the Vijaya Dasami day. Special pujas are held on the day dedicated to this form of Durga in Orissa, Jharkhand, Bengal and other parts of eastern India.
There is also a belief is some Hindus that Goddess Aparajita resides in the Shami Tree. Shami Puja is also held on the Vijayadasami day.
In Jainism, there is a Goddess known as Aparajita and she is a Yakshi or demi goddess.
An Vrata dedicated to the goddess known as Aparajita Saptami Vrata is observed on the seventh day during the waxing of light phase of moon in Bhadrapad month (August - September) - Bhadrapad Shukla Paksha Pratipada tithi.