A student named Sarah Batte appears in the rolls of the Mordecai school. She attended for the last two sessions of the school, in 1818. She's listed as being from Bellfield and an Alexander Batte is the adult name on the account.
Alexander Watson Batte (1778-1853) of Greensville County VA seems a good candidate for the adult--he married his first wife, Mary Pettway, in 1803, which would be time enough for their daughter to be at the school in 1818. The Alexander Watson Batte House in Greensville County was built starting in 1815. He married his second wife Elizabeth Spencer in 1819, so presumably Mary Pettway Batte died in 1818 or earlier--providing a reason for the girl to be at school (many of the Mordecai students were there following the death of a parent, while practical arrangements were made at home). And there is a Belfield District in Greensville County--it was a town before 1887 when it merged with Hicksford to form Emporia.
Still, can't find any evidence of a daughter named Sarah, born to Alexander and Mary Pettway Batte. There's only mention of Alexander Batte's daughter Cornelia Alvinia Batte, born 1819, so her mother was Elizabeth Spencer. So Sarah might have been a niece or other kin.