That’s a question I’m often asked by my students and here’s the answer I offer them.

What kind of “corner” are you referring to? Is it the corner of a room or the corner of a street?

♥ If you are giving directions  to a shop, then you should say:

This shop is on the corner of High Street

♥ If you are saying that a person is sitting in a chair in a room, then:

Mary is sitting in a chair in the corner of the sitting-room.

Summarising: you use in, when the corner is inside and on, when the corner is outside.

Note: you can also say at the corner to refer to the corner of a street.

I’ll wait at the corner/ I’ll wait on the corner.