The Brahma Sampraday is one of the Bairagi Naga class's four branches of ascetics.
The Bairagi Nagas are followers (bhakta) of the deity Vishnu who are arranged into various anis, or "armies," in a military manner.
Their main profession until the beginning of the nineteenth century was as mercenary warriors, but they also had significant trade interests; both of these vocations have virtually vanished in modern times.
The Brahma Sampraday may trace its spiritual ancestry back to the Bengali follower Chaitanya's Gaudiya Vaishnava sect, but it claims ultimate origin from the southern Indian scholar Madhva.
This second assertion seems dubious, in part because the two sects' guardian deities are different: Chaitanya and his followers worship the gods Krishna and Radha, while Madhva and his followers worship Lakshmi-Narayan.
There are also distinctions in their practices.
The Madhva ascetics have a lengthy history in southern India, but they are practically unknown in the north, where the Chaitanyite ascetics are well-represented.
Ghurye speculates that the Gaudiya Vaishnavas' claim is based on their desire to create connections to an old lineage, which would provide them with an unquestionable identity and therefore a position in the Kumbha Mela bathing (snana) procession.
Recommended read - Indian Sadhus, by G. S. Ghurye, 1964.