Let's say someone asks you where you go to school:
I'm a student at Suffern High School.
Let's say you're at a competition with one student from each of several school. The organizer says "I need the student from Suffern. Where's Suffern's representative?"
I"m the student from Suffern.
I can't make "I'm the student at... " sound normal unless it one a one-student school.
I wouldn't use"of."
Student or Learner