Branches of Yajurveda are explained in Vishnu Purana. Chapter Five of Part three in Vishnu Purana explains about the branches of Yajurveda.
A disciple of Veda Vyasa named Vaishampayan created twenty-seven branches of Yajurveda and taught them to his disciples. He had a disciple Yagyavalkya who was the son of Brahmarat. At that time, all the sages together constituted a rule that whoever did not join their group within seven days on Mahameru would be held as a sinner equal to killing a Brahmin. Only Vaishampayan had violated that ruling. The curse of the sages did come true when Vaishampayan killed his sleeping nephew accidentally. Then he asked his disciples to do away with his sin.
Yagyavalkya said- “Lord! All these Brahmins are extremely dull. I will alone do away with your sin.” These boastful words infuriated Vaishampayan. He said- “You are insulting these Brahmins so at once, regurgitate whatever I have taught you.” Yagyavalkya said- “Lord! I uttered these words out of devotion for you. Still you wish me to regurgitate what you have taught me. Here it is! Saying this, Yagyavalkya vomited out all the Shrutis of Yajurveda. Other disciples of Vaishampayan pecked them in the form of partridges. Since then, they came to be known as Taitriya Brahmins. Holding his breath, Yagyavalkya then started the worship of the Sun with a desire to regain Yajurveda.
Pleased by his prayers, Surya appeared before him in horse form and asked him to seek a boon. Yagyavalkya requested Surya to preach him those Shrutis of Yajurveda, which were not known
even to his teacher, Vaishampayan. Surya preached him those Shrutis of Yajurveda, which were known as Ayatyam. The Brahmins who read these Shrutis came to be known as Vaji. Nowadays, there are fifteen sub-branches of these Vaji Shrutis, which were initially expounded by sage Yagyavalkya.