The first Mordecai student, alphabetically, is the wonderfully named "Narcissa Abernathy." From the school's records (mostly the ledger), I can say for certain that she was from a place called "Brunswick" and that a William Abernathy was her parent or guardian, and that she stayed at the school for its last two semesters: spring and fall of 1818.
"Brunswick" can mean two different likely hometowns: Brunswick County NC is in the southeastern part of the state, near Wilmington and the South Carolina border. Brunswick County VA is just over the NC/VA border from Warren County. Both places sent students the Mordecai school, but the Virginia Brunswick was closer, and has the added factor of an Abernathy family that was prominent at the time. So I'd probably assume she's a Virginia girl.
Let's see what the genealogical forums have to say: It seems there was a Narcissa Abernathy whose parents were William "Poplar Mound Billy" Abernathy (d. 1844) and his wife Nancy; who had sisters Marianne, Dionysia, and Arianna, and brothers William and Willis; who married her cousin James Abernathy Jr. by 1822, in Greensville County, VA. The couple moved to Giles County TN around 1827, and had about five children (Virginia, Martha Ann, John, William, and Samuel). She would have been widowed around 1845.
Those dates and details would make sense for a Mordecai student--a lot of Mordecai girls married in the early 1820s and moved west soon after. Is it her? I wouldn't know for sure without some family history or letters mentioning her being the same person; but I think this is a good tentative match, given her unusual name and the matches in age, placename, and father's name.