It is said that Jay and Vijay are the gatekeepers of Vaikuntha Lok where Lord Vishnu resides. they are called as Dwarpaals, which literally means guard of the door or gate. Once they prevented some sages and Maharishis from seeing Lord Vishnu and seeking his blessings. The Maharishis cursed them for this reason. Because of this curse, they were destined to be reborn as demons. You are probably familiar with this story. If not, keep listening, because this is the part where today's episode gets really interesting.
When Lord Vishnu came to know about this curse, he gave a choice to his two gatekeepers. In the first option, they could be born as demons for three lifetimes. After which, they could return to Vaikuntha. In the second option, they could have been born as great devotees of Lord Vishnu. If he chose the second option, he was required to be born seven times.
Jai and Vijay chose the first option, because by choosing the first option they could soon return to the abode of Lord Vishnu. And thus Jai and Vijay were born as demons in three different eras. Since each birth took place in a different era, with each birth the strength and wickedness of the demons diminished.
In every birth, Jai and Vijay were born as mighty demons, and in each of the three births, two demons created havoc. In the first birth, he was born as Hiranyakashipu and Hiranyaksha as Satya Yuga. To kill these two, Lord Vishnu had to take two incarnations. Hiranyaksha was killed when Lord Vishnu incarnated as Varaha and Hiranyakashipu was killed by Narasimha.
In Treta Yuga, Jai and Vijay were born as Ravana and Kumbhakarna. They were killed by Lord Rama. In Dwapar Yuga, Jai and Vijay were born as human beings, namely Dantavakra and Shishupala. He was killed by Krishna.