According to this YouTube Video, There are 8 children of Shiva. While 7 are known ones, but the last one is devi Jyoti, also known as Jwalamukhi and Rayaki. Can somebody share scriptural reference of her being daughter of Shiva and Parvati and how was she manifested?
In Shiva Purana, Jwalamukhi Devi is mentioned to be born/created out of the fire in Goddess Sati's body. This was during the event of destruction of Daksha Yajna.
Even as the whole of the world of Devas was witnessing, the process of destruction of the sacrifice was carried out by Vīrabhadra and others, the followers of Rudra.
The policy in agreement with what is laid down in the Vedas and Smṛtis is this, O Sage, which you must note. When lord Rudra is angry, how can there be happiness in the world?
On hearing his song of praise Rudra relented. Favourably disposed to the miserable that he was, he granted their request.
Śiva, the great lord, indulging in different sorts of divine sports, became sympathetic and merciful as before.
Dakṣa was resuscitated. The whole sacrifice was renewed under the instruction of the merciful Lord Śiva. All those present were honoured in due manner.
O sage, in that sacrifice Rudra was honoured by all the Gods with due devotion. They were highly delighted.
41. The flame of fire arising from the body of Satī and delighting the whole world fell on that mountain and it was duly worshipped.
42. The deity became famous as Jvālāmukhī yielding fruits of cherished desires. Even her very vision quells all sins.
Since the Devi was born out of Goddess Sati, she can be considered as a 'child" of Sati and hence that of Lord Shiva too.
She has been mentioned in Skanda Purana too.
Quoting from the "Essence of the Skanda Purana":
‘Tripuranthak Kshetra’ where the Three Eyed Siva demolishes the devotees’ fear of ‘Naraka’; ‘Prabhasa Kshetra’where Sri Krishna and Balabhadra worship ‘Chandrardha Sekhar’; ‘Jaalandhar kshetra’where Andhakasura was killed by Siva and Jalandhar did Tapasya to become the Head of ‘Shivaganas’; ‘Jwalamukhi’ Sthaan ( Place) where Devi Jwalamukhi worships ‘Kaala Rudra’; ‘Triambakeswar’ on the banks of Godavari River where Kartikeya secured the Shakti to kill Tarakasura and so on.
Quite possible that more details about her are mentioned in various other Puranas too.