As I discuss in this answer, how the Vedas originated is that from time immemorial, sages known as Dhrishtas heard sacred verses directly from the gods during a state of Tapasya (deep meditation), and then in the Dwapara Yuga they were compiled into the four books we call the Vedas. But this chapter of the Apastamba Dharma Sutras, a text associated with the Yajur Veda, says that such sages are not born in the Kali Yuga:
On account of that (transgression of the rules of studentship) no Rishis are born amongst the men of later ages.
But some in their new birth, on account of a residue of the merit acquired by their actions (in former lives), become (similar to) Rishis by their knowledge (of the Veda),
Here is what Haradatta says in his commentary on these Sutras:
Amongst the avaras means "amongst the men of modern times, those who live in the Kaliyuga." No Rishis are born means "there are none who see (receive the revelation of) Mantras, Vedic texts." ...
How is it then that men in our days, though they transgress the rules prescribed for students, learn the four Vedas with little trouble? (The answer is), By virtue of a residue of the reward (due) for the proper observance of those rules (of studentship) in a former Yuga. Therefore Âpastamba says, Sûtra 6 "But some," &c. New existence means "new birth (life)." ...
Like Svetaketu. For Svetaketu learned the four Vedas in a short time; as we read in the Khândogya Upanishad (Prapâthaka VI, 1).
As I discuss in this question, Shwetaketu is the son of the sage Uddalaka Aruni. An important part of the Chandogya Upanishad is a dialogue between Shwetaketu and his father, during which the famous Mahavakya "Tat Tvam Asi" is mentioned.
But my question is, what Yuga was Shwetaketu born in? The reason I ask is that the Apastamba Dharma Sutras seem to be saying that Shwetaketu is an example of the kind of person who was born in the Kali Yuga, but was still able to learn the Vedas quickly like a Rishi would due to his actions in a past birth. And indeed, this chapter of the Chandogya Upanishad says Shwetaketu learned the Vedas in a mere 12 years, whereas the standard pace for learning all four Vedas is 48 years.
Yet in this chapter of the Adi Parva of the Mahabharata, Pandu describes Shwetaketu as someone who was born in the distant past:
It hath been heard by us that there was a great Rishi of the name of Uddalaka, who had a son named Swetaketu who also was an ascetic of merit.... Thus, O timid one, was the existing usage established of old by Swetaketu, the son of Uddalaka, in defiance of antiquity.
So considering that Pandu lived in the Dwapara Yuga, Shwetaketu cannot have been born in the present Kali Yuga. So is it possible that he was born in some past Kali Yuga? If so, which Mahayuga was he born in?
The only clue I've come across is the fact that Shwetaketu was the uncle of the sage Ashtavakra, purported author of the Ashtavakra Gita, and Ashtavakra visited the court of a king named Janaka. But it's not clear to me whether this refers to the famous father of Sita, because pretty much all the kings of Mithila were known by the name Janaka. The Janaka visited by Ashtavakra is probably the same Janaka mentioned in the Upanishads, but I don't know whether this Janaka is the same as the father of Sita, whose given name was Siradhvaja.
By the way, on a side note Shwetaketu was not the biological son of Uddalaka Aruni, as I discuss here.