"vasara peeta nilaye" in the sloka indicates that Saraswati is the presiding deity of Vaasara kshetra, now Baasara kshetra, a temple town in Northern parts of Telangana state.
The legend has it that after the Mahabharata war, sage Veda Vyasa embarked on a pilgrimage in search of peace. He reached the serene Kumaranchala hills on the banks of river Godavari and meditated and propitiated the Goddess who eventually appeared before him and granted her presence in the form of the divine trinity.
The Goddess ordered the sage to place three handful of sand at three places everyday. Miraculously these sand dunes transformed into the idols of the divine trinity i.e., Saraswathi, Lakshmi, & Kali.
These are the presiding deities of Basar today. Despite the presence of the trinity,the temple is dedicated to Goddess Saraswathi.
Children are brought here for the ceremony of Akshara puja to start their education with the blessings of the Goddess of Knowledge.The Vedavathi Sila, the Ashtateertha are other places of interest around Basar. Thousands of devotees bath in the river Godavari & seek the blessings of the Goddess during the Mahashivarathri, Dassera navratris and Vasantha panchami.
This sloka basically composed to eulogise Saraswati devi of vAsara , now bAsara kshetra.
As is the tradition, here also Saraswati devi's form was eulogised as equal as beautiful as Autumn's moon - sharadindu samAkAre.
manifestation of parabrahma - parabrahma swaroopine