According to Matsyapurāṇa (Matsyapurana), Āyuṣmān (Ayushman) is the son of Prahlāda (Prahlada), the king of Daitya (a type of Demons).

Matsyapurāṇa(6.9)

According to Viṣṇupurāṇa (Vishnupurana), Āyuṣmān(Ayshman) is the son of Saṁhlāda (Samhlada).

Viṣṇupurāṇa(1.21.1)