What was the story of Adhoksaja, an incarnation of Vishnu. In which Puranas is the name Adhoksaja mentioned? Why did Vishnu take the incarnation?
The name Adhokshaja is the name of Bhagavan that glorifies his Shakatabhanjana leela. As per the Harivamsa:
अत्यद्भुतमिदं चासीद्यच्छिषुः पुरुषोत्तमः॥
पादाङ्गुष्ठेन शकटं क्रीडमानो व्यलोडयत्।
He was born again, so people said, and that is why he was called as Adhoksaja. It was such a wonder that the best among men as a child upturned a cart with the toes of his feet, as if while playing.
-Harivamsa, Vishnu Parva, 101.33-34
The Shakatabhanjana story has been described very beautifully in the Bhagavatam. It was during the performance of the Utthana ceremony when a sleepy Bhagavan was kept down under a cart by Yashoda and lo:
The liberal mother Yaśodā, absorbed in celebrating the utthāna ceremony, was busy receiving guests, worshiping them with all respect and offering them clothing, cows, garlands and grains. Thus she could not hear the child crying for His mother. At that time, the child Kṛṣṇa, demanding to drink the milk of His mother’s breast, angrily threw His legs upward. Lord Śrī Kṛṣṇa was lying down underneath the handcart in one corner of the courtyard, and although His little legs were as soft as leaves, when He struck the cart with His legs, it turned over violently and collapsed. The wheels separated from the axle, the hubs and spokes fell apart, and the pole of the handcart broke. On the cart there were many little utensils made of various metals, and all of them scattered hither and thither.
The residents of Vraja, unaware of the child’s power could not believe how the child had been saved by such a violent upturn of the cart. They thus considered as if he had gotten a second birth hence was glorified with the name, Adhokshaja where; Adhah means below, Aksha means axle, and ja indictes born.
Adhokshaja is the child who was born again below the axle.