As I discuss in this answer, Hindu scripture is made up of two categories, Shruti or that which is heard from the gods, and Smriti or that which is composed by humans authors and passed down from teacher to student via oral tradition. It's well-known that Smriti encompasses many different categories of texts, like the Puranas, Itihasas (the Ramayana and Mahabharata), Dharma Shastras, etc. What's not as well-known, however, is that Shruti also has two categories - Nigamas aka the Vedas which primarily focus on performing Yagnas (fire-rituals), and Agamas which focus on worshipping the gods through idol worship and other means.
Now the vast majority of mainstream Vaishnavas follow a set of Agamic texts known as the Pancharatra Agamas, which I discuss in this answer. And as I discuss here, there's a small minority of Vishnu-worshippers that follow another set of Agamas called the Vaikhanasa templs. For instance, the most popular Vishnu temple in the world, the Tirumala Venkateshwara Temple, is run by Vaikhanasa priests.
I assumed that these were the only types of Vaishnava Agamas, but this essay by Swami Sivananda says otherwise:
The Vaishnava Agamas are of four kinds: the Vaikhanasa, Pancharatra, Pratishthasara and Vijnanalalita.
Lots of other websites make the same claim. So my question is, what are the Pratishthasara Agamas and the Vijnanalalita Agamas? Are there any Vishnu temples that follow them? Are there Vaishnava sects that follow them? It would have to be some pretty tiny sects, given that the overwhelming majority of Vaishnavas follow Pancharatra Agamas.
Also, what are the origins of these Agamas? As I discuss in this question, the Pancharatra Agamas are said to originate from a Shakha or recession of the Shukla Yajur Veda, and the Vaikhanas are said to originate from a Shakha of the Krishna Yajur Vedas. Do the Pratishthasara and Vijnanalalita Agamas also originate from Vedic Shakhas? (See my answer here for more information on Vedic Shakhas.)