In which Yuga was Tarakasur born?
Was he born in Satya Yuga, Dwapara Yuga, Tetra Yuga and which Maha Yuga of which Manavtar?
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Here is how Tarakasur born according to Padmapuran
Sage Kashyap blessed his wife Diti to give birth to a great warrior ‘Vajranga’ who like a diamond was unbreakable and indestructible. Diti desired to avenge the killing of several Asuras in the past by Indra and asked Vajranga to defeat and bring down Indra imprisoned in person; on doing so, Diti put Indra to shame and released him saying that his subduing was worse than his death.
Meanwhile, Vajranga did severe Tapasya to Brahma and the latter created Varangi as the wife of Vajranga. Brahma gave a boon to the pair that a Maha Shaktivaan called Tarakasura would be born after being retained for thousand years in confinement. There were harsh earthquakes and sea-uprisings when the Asura was born and the parents were filled with wild joy and excitement. As the boy attained youth, he turned out to be a frightening demon and developed friendship with other Asuras like Kujambha and Mahisha. Eventually, he reached a Pariyatra Mountain to perform Tapasya without food for hundred years, for another hundred years by consuming only dried leaves and for additional years by drinking water only. Brahma was pleased and gave a boon of invincibility except for a child of seven days of age, to be born of Shiva. After securing the boon from Brahma, Tarakasura raised a huge army of ten crore well-versed and trained soldiers along with the armies of renowned Asuras like Mahisha, Kunjara, Megha, Kaalanemi, Nimi, Manthana, Jambhaka and Sumbha. As Tarakaura declared war with Indra and Devas, Indra commissioned Vayu Deva as an emissary as per the advice of Deva Guru Brishaspati, but the mission failed and so did the proverbial Four ways of ‘Rajaniti’ or the Art of Politics viz. Sama (War-Counselling), Daana (luring by gifts), Bheda or by using the dividing politics of the opponents and Associates and finlally ‘danda’ or actual war. Yamaraja was the Senapati, the Commander sitting over his Vahana Buffalo; Indra sat on his Durjayta ratha (chariot) with Malini as his driver; and all other Devas like Agni, Vayu, Varuna, Kubera, Chandra and Aditya, besides Ashvini Kumars, Marudganas, Sandhyaganas, Yakshas, Gandharvas etc. But Tarakasura was too powerful to Devas whose soldiers were badly bruised and ran without direction. Indra and Devas approached Brahma and he replied that none excepting a seven day son of Shiva and Devi Parvati, called ‘Kartikeya’ could kill Tarakasura and none else in the world.
According to Skandapurana Tarakasura born after the death of Sati And According to a legend mentioned in Devi Puran, during Sat Yuga, Daksha (son of Lord Brahma) performed a yagna in a place called Kankan (near Haridwar). He performed this Yagna with a desire of taking revenge on Lord Shiva. Daksha was angry because his daughter Sati (one of his 27 daughters) had married Shiva against his wishes. Daksha invited all the deities to the yagna except for Shiva and Sati. The fact that she was not invited did not deter Sati from attending the yagna. Sati, being an uninvited guest, was ignored by her father. Moreover, Daksha went on to insult Shiva. Sati could not bear her husband’s insult, so she committed suicide by jumping into the yagna fire. Here is Another Source from Skandapurana
That's why i mentioned it that Tarakasura was born in Sat Yuga
After the death of Sati, Lord Shiva became aloof and engaged himself in an austere penance. His lack of interest in performing his duties resulted into the predominance of sin in the world.A demon named Tarakasur had received a boon of invincibility from lord Brahma. Only a child and nobody else could kill him. Tarakasur, being drunk with power started to torment the deities.