The passage of time appears to have obscured the existence and importance of the Gadādhara parivāra. The word parivāra means family. This parivāra was started by Śrīla Gadādhara Paṇḍit Gosvāmī, who out of respect, is simply known as Paṇḍit Gosvāmī.
Śrī Babaji writes:
“At one time, only Paṇḍit Gosvāmī’s parivāra was prominent in Vṛndāvana. Śrī Narottama dasa Thakur writes in one song that the Gosvāmī of Vrindavan are followers of Paṇḍit Gosvāmī. He also writes that he himself belongs to the family of Paṇḍit Gosvāmī. This period lasted for about two generations. Then things changed and Paṇḍit Gosvāmī’s importance was forgotten.”
Based on my experience, the parivāra’s emphasis is on faith in and study of the scriptures, and performing bhakti accordingly. The specialty of the parivāra is that members do not run after money, preaching or cheating others. Being part of the parivāra and learning in it transports one back to the time of the Gosvāmīs. The foundational books of the parivāra are the books of the Gosvāmīs, in particular, Śrī Rūpa and Śrī Jīva Gosvāmī. The paramparā has (thankfully) preserved traditional understanding of the Sandarbhas meticulously, which is now available in Śrī Babaji‘s English translations.
The line of Paṇḍit Goswami
Here is what Śrī Maharrajji said about the parivāra:
“When Śrī Caitanya Mahāprabhu started his movement, he specifically appointed Paṇdit Goswami to give dikṣā. Mahāprabhu personally gave him the deity to worship and the responsibility to teach Bhāgavata purāṇa. Mahāprabhu used to hear Bhāgavatam from Paṇḍit Goswami to set an example for others. Therefore, originally, Paṇḍit Goswami initiated all the Goswamis and even other devotees. The temples in Vṛndāvana as well as Rādha Kuṇda were made by the Goswamis, and they were all disciples of Paṇḍit Goswami. Rādha Kuṇda originally belonged to Raghunāth das Goswami, who came in the line of Paṇḍit Goswami.” — Śrīla Haridasa Śāstrī Māhārajji

The lineage of the parivāra that Śrī Babaji is part of is as follows:
- Śrīla Gadādhara Paṇḍit Gosvāmī
2. Śrīla Bhūgarbha Gosvāmī
3. Śrīla Caitanya Gosvāmī
4. Śrīla Bhīmānanda Gosvāmī
5. Śrīla Kāśīrām Gosvāmī
6. Śrīmatī Svarṇamaṇi Gosvāminī
7. Śrīmatī Hemamaṇi Gosvāminī
8. Śrīmatī Kiraṇamaṇi Gosvāminī
9. Śrīmatī Cintāmaṇi Gosvāminī
10. Śrīla Durgānātha Gosvāmī
11. Śrīla Vinoda Vihārī Gosvāmī
12. Śrīla Haridasa Śāstrī Māhārajji
13. Śrīla Satyanārāyaṇa dāsa Bābāji
Categories: sādhanā
With luminaries like Sri Haridas shastri Maharaj and Sri Satyanarayana Dasa Babaji Maharaja appearing in this parivara in recent times and producing luminous literary treasures, the Gadadhara parivara’s glory will surely shine forth yet again.
Is Śrīla Satyanārāyaṇa dāsa Bābāji giving Diksha to new disciples? Who will continue the The Gadādhara parivāra after him?
Answering both your questions is above my pay grade. Best to ask him directly.
There are many gurus in Gadadhara parivara.
Hope this Parivar expands soon. Babaji’s knowledge is amazing.