Though Singapore Traffic Police should be the only body to fine issues, but it was not always the case.
Carpark lots under Housing Development Board (HDB) is under their jurisdiction which they have engaged external parties to check on vehicles that park illegally or did not use a parking coupon when the vehicle was being parked.
In some of the area, Certis Cisco are also being engaged by the government to look after the roads and to check for illegal parking or parking without valid coupon.
The fine amount varies largely to the offence committed, ranging from $25 to $300. I have screenshot a list of offence and the fine amount as shown below. Taking a good look below, you get a hefty fine for trying to cheat the law or you can't speak well and explain why the official coupon wasn't there. Better not to try your luck.