You can say both:
"the shop on the corner"
and "the shop at the corner"
but "the shop on the corner" is more common!
(The latter is almost a cliche; but "the shop at the corner" is perfectly English.)
You can also say,
"The shop is on the corner of Main and 2nd."
"The shop is at the corner of Main and 2nd."
However you say:
"I'll be at the corner store"
(which means in front of it or inside of it)
but certainly not "on the corner store" which sounds like you are on the roof of the store!
You use "at" when you are talking about a person's location with respect to a building;
you cannot use "on" if the person is at a store because like I said, that means on the roof!
But "He's hanging out on the corner" is fine.
And "He's standing at the corner of Main and 2nd" is fine.
Don't say "in the corner"
unless you mean in the corner of a box (inside a box) or room (inside the room),
"The teacher asked him to stand in the corner and say he was sorry for fighting."
For more "on the corner," see the Credence Clearwater (I did like CCR as a kid):
some of the lyrics will not make sense, but on and in are used correctly! at is not used in this song alas!
--C. E. Whiteherad