Frogs occupy a strange and specific position in Indic religious history. They aren’t gods (mostly), they have no cult. But they show up in the Rig Veda chanting like Brahmins, in the Śatapatha Brāhmaṇa as the literal runoff of the primordial Agni, in the Atharvan ritual manuals as a receptacle for fever, in the Mahābhārata as a kingdom with a king and ambassadors, and in both Buddhist and Jain scripture as creatures with minds, with souls, who can take vows, and who can get to heaven. What follows is an attempt to lay out the references, and point out some patterns which emerge.

Satapatha Brahmana
Here’s an interesting Vedic passage referencing frogs, from the Śatapatha Brāhmaṇa (of the Śukla Yajurveda):
19. ‘The widely-shining by name,’–for the gods then called those bricks to them by their names, and in the same way in which they called them, they turned unto them; but the ‘space-fillers’ alone stood with averted faces discharging water, having no names applied to them. They called them by the name ‘the widely-shining,’ and they turned unto them. Hence, each time he has laid down ten bricks, he addresses them with the ‘space-filling 1 (verse)’: he thereby makes them widely-shining (virâg), for the Virâg (metre) consists of ten syllables:–‘wish-milking, never-failing,’–he thereby makes them wish-milking and never-failing.
20. He then draws a frog, a lotus-flower, and a bamboo-shoot across (the central part of the altar). For the gods having now appeased him by the Satarudriya and the water, and having driven out his pain and evil, thereby still further appeased him; and in like manner does this (Sacrificer), now that he has appeased him by the Satarudriya and the water, and driven out his pain and evil, still further appease him thereby. In every direction he draws them: he thus appeases him everywhere.
21. And, again, as to why he draws them across. Now, in the beginning, when the Rishis, the vital airs, made up that Agni 2, they sprinkled him with water: that water dripped off and became the frogs.
22. They (the waters) said to Pragâpati, ‘Whatever moisture 1 we had, has gone down.’ He said, ‘This tree shall know it!’–he shall know (vettu), he shall taste it (sam vettu)–that one, indeed, they mystically call ‘vetasa’ (bamboo), for the gods love the mystic. And because they said, ‘Down (avâk) has gone our moisture (ka),’ they became avâkkâs;–‘avâkkâs,’ they mystically call ‘avakâs (lotuses),’ for the gods love the mystic. These, then, are those three kinds of water, to wit, the frog, the lotus-flower, and the bamboo-shoot: by means of these three kinds of water he appeases him.
23. And, again, why he draws them across it;–when he (Agni, the fire-altar) is built up, he is being born, and he is born for every kind of food; and these are every kind of food, to wit, the frog, the lotus-flower, and the bamboo-shoot, for these, indeed, are animals, water, and trees: with all this food he gratifies him.
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