I have a student in the rolls for the Mordecai school named Mary Connick. No hometown, no adult name attached to the account. She seems to have been at the school in 1809 (its first year), and then later for the first half of 1811. That pattern sounds like a local girl...
I think she only turns up once in my transcripts of the Mordecai papers--1.50 for pocket money for "M. Connick" is in the school ledger for May 1811. That's it. Not much to work with there.
Connick is an established surname--think Harry Connick Jr., for one--but it's possible that the name Connick was misspelled by the Mordecais, or misread by me. Maybe it should be Cormack, or Connaught? Not seeing any likely candidates, with any variation. Trying Polly (a common nickname for Mary at the time)... Okay, well, there's a Polly Cormack born 1797 (which would be the right year for a 1809-1811 student), born in North Carolina, daughter of Lewis Cormack (1769-1842) and Esther; but it looks like their family had moved to Tennesee by 1805. Probably not her.
Too many dead ends for now to connect Mary Connick the student to anyone in other records. We'll wait and see if anyone comes along who know's more.