Boarding passes (plane ticket) list both the gate and your assigned seat. In this case, it was probably a larger airport with multiple terminals labeled A, B, C, etc., so the plane was at gate 3 in terminal C (hence; gate C3). This was confused with the seat assignment, which is always labeled A, B, C, etc. (for the row) and 1, 2, 3, etc. (for the column). Seat map example

Here’s an example of a boarding pass, notice the gate number on the left and seat number on the right, both in the same letter-number format