at the side of something—situated or placed beside smth.:
- He fancied he heard the tramp of a troop of horse at the side of the wood.
on the side of something—
1. = at the side of something:
- As I was driving I passed the car on the side of the road again. This time the lights were not on.
2. on the side surface of smth.:
- The Stock Exchange waiter strikes three strokes with a mallet on the side of a rostrum before making formal declaration.
3. supporting smth.; in favor of smth.:
- Normally, and as a whole, human law is on the side of divine order.