"Jitiya fast" & its roots from "Mahabharata"
"Jivitputrika Vrat" aka "Jitiya vrat" is a festival which is mainly observed in the states of Bihar, Uttarpradesh & Jharkhand. This Festival is basically a day when every mother holds a whole day Nirjala(no water consumption) fast for the longevity of her offsprings. This fast is performed on the ashtami of the Krishna paksh of Ashwin Mas.
The origination of this fasting hails from the period of "Mahabharata". Ashwatthama was very angry after his father's death in the war & with a sense of revenge in his mind, he entered the Pandavas camp. He saw 5 people sleeping there & considering those 5 people as "Pandavas", he killed all of them but those 5 were actually the sons of the Pandavas. He also used his Brahmastra to kill the unborn baby in Uttara's womb (Uttara, the widow of Abhimanyu). Lord Shri Krishna used his divine powers to restore the life of Uttara's unborn child.The child, who was alive by the grace of Lord Krishna, was named Jivitputrika. Since then, the tradition of keeping the Jitia vrat vow every year for the longevity of the children.