Question: During which of the 4 Yugas did the churning of the milk ocean take place?
Answer by Romapada Swami:
Based on search results thus far, Śrīmad Bhāgavatam records that the churning of Milk Ocean took place during the Cākṣuṣa manvantara (SB 8.5.8-10), but Srimad Bhagavatam does not mention the yuga in which it took place. A verse in Rāmāyaṇa indicates that the incident took place in Satya-yuga (a.k.a. Kṛta-yuga).
In Rāmāyaṇa, Bāla-kaṇḍa, Chapter 45, on their way to Mithila to visit King Janaka, Viśvāmitra relates to the two young princes, Rāma and Lakṣmaṇa, the history of the churning of the milk ocean, which leads to fierce combat between the Devatas and the Daityas.
Verse 15
pūrvaṁ kṛtayuge rāma diteḥ putrā mahābalāḥ
aditeś ca mahābhāgā vīryavantaḥ sudhārmikāḥ
Formerly in Kṛta-yuga, O Rāma, the sons of Diti were very powerful. The sons of Aditi were also highly fortunate, valiant and most righteous.
Verse 16
tatas teṣāṁ naraśreṣṭha buddhir āsīn mahātmanām
amarā nirjarāś caiva kathaṁ syāma nirāmayāḥ
In the course of time, O tiger among men, it occurred to those great personages: How can we become immortal, youthful and free from disease?
Verse 17
teṣāṁ cintayatāṁ rāma buddhir āsīd vipaścitām
kṣīrodamathanaṁ kṛtvā rasaṁ prāpsyāma tatra vai
As they were contemplating this, the following thought occurred to them: If we churn the ocean of milk, we shall certainly obtain the elixir of immortality.
Verse 18
tato niścitya mathanaṁ yoktraṁ kṛtvā ca vāsukim
manthānaṁ mandaraṁ kṛtvā mamanthur amitaujasaḥ
After deciding to churn the ocean of milk, those beings whose splendor was immeasurable took Mount Mandara as the churning rod and the celestial serpent Vāsuki as the rope and began churning.