As Wikipedia says:
Tripurāsundarī (त्रिपुरा सुंदरी - "Beautiful (Goddess) of the Three Worlds") or Mahā-Tripurasundarī ("Great Beautiful (Goddess) of the Three Worlds"), also called Ṣhoḍaśhi ("Sixteen"), Lalitā and Rājarājeśvarī ("Queen of Queens, Supreme Ruler"), is one of the group of ten goddesses of Hindu belief, collectively called Mahavidyas or Dasha-Mahavidyas. She is the foremost and the most important in Dasha-Mahavidyas.
There was a demon by the name of Bhandasura who got boon from Brahma that he would die only at the hands of a woman who wasn't given birth to by another woman.
The story goes like this:-
Lord Shiva, upon hearing the troubles caused by Bhandasura to the demigods reminded Goddess Parvati about Brahma's boon. Parvati realizes that she was the unborn universal power who alone could kill Bhandasura as she was Adi-Shakti. But as parvati she was still the child of Himavan and Menavati. So, Upon her and Lord Shiva's command, the demigods prayed to the supreme Brahman Sadashiva who manifested before them in two forms: Shambhu and Shakti. The Saptarishis were ordered to perform a fire sacrifice which would help Shakti manifest. During the sacrifice, all the deities entered the fire, and from their bodies, the body of the world's most beautiful being, Tripurasundari was created. She then recreated Vishnu and Parvati (Brother and sister), Brahma and Saraswathi and Rudra and Lakshmi in that order followed by all the other demigods.
Similar version of this story:-
The devas faced an enemy in Tarakasura who had a boon that he could be killed only by a son of Shiva and Parvati. So for the purpose of begetting a son from Shiva and Parvati, the devas deputed Manmatha, the God of love. Manmatha shot his flower arrows to Shiva and Parvati in order to induce severe sexual feelings in them. Shiva in anger for being tricked, opened his third eye which reduced the God of love to ashes. The Devas and Rathi Devi, the wife of Manmatha requested Shiva to give life to Manmatha. Heeding their request Shiva stared at the ashes of Manmatha. From the ashes came Bhandasura, who made all the world impotent and ruled from the city called Shonitha pura, after which he started troubling the devas. The devas then sought the advice of Sage Narada and Trimurti, who advised them to seek the help of Nirguna Brahman, the ultimate god head which is unmanifested i.e. Sat-Chit-Ananada (Truth-Consciousness-Bliss). Nirguna Brahman took the shape of Maha Sambhu and Adi Parasakthi (who were unmanifested and beyond the manifest Brahmanda) and appeared before them. Maha Sambhu and Adi Parasakthi agreed to take the form of Maha Kameswara and Lalita Tripura Sundari for the benefit of the universe. For this a maha yajna is made where the entire creation i.e. manifest universe is offered as the oblation and from the fire rose Maha Sambhu and Adi Parasakthi as Lalitha Tripura Sundari and Kameswara.Lalitha Tripura Sundari and Kameswara re-created the entire universe as it was before. She created Brahma and Lakshmi, Vishnu and Parvati, Shiva and Sarswati.Thus Vishnu came to be known as the brother of Parvati (i.e. incarnation of Lalita or Adi Para Sakthi).
My question is how can someone say to Nirguna Brahman "Hey Nirguna Brahman, become Saguna Brahman". That sounds completely ridiculous to me. Shakti could still kill Bhandasura because Parvati was born, Shakti was not. So the boon by Brahma can't help Bhandasura, and even if Parvati can't kill him then Tripura Sundari can't kill him either.
Tripura Sundari Ashtakam(Adi Shankara):-
I seek refuge in the immaculate and beautiful Mother, Who has a Veena (lute) honored at Her breasts, Who is decorated with curly tress-locks, Who resides in water-lily petals, Who is inimical to cunning minds, Who has eyes which are red as due to wine-consumption, Who entices the destroyer of Manasija or Kamadev (Shiv), Who is the daughter of Sage Matanga (as Matangi), and Who speaks mellifluously.||5||
Now Adi Shankara says Tripura Sundari was daughter of Sage Matanga! This clearly contradicts the above Wikipedia text. And if I have to choose one, I would obviously believe Adi Shankara's words.
So are there any scriptures which say Tripura Sundari came out of the Maha Yajna or was the daughter of Sage Matanga as Adi Shankara says?