You are very wise to want to change the habit. The high sugar content in candy, cookies, ice cream and many processed foods like chips, packaged meals and "fruity" yogurts is very damaging to the teeth. especially baby teeth, which have quite thin enamel. Sticky sweets like caramel, gummy bears and even raisins are the worst, because the sugar is "glued" to the teeth, often for hours.
So, how to change? Most 5-year olds (let alone almost-fours) have little understanding of long, elaborate explanations of rules, expectations, or consequences. You can tell her that you asked Dr. Smile (or whoever her dentist is) about the candy treat, and she told you that it would make holes in her teeth, so you can't give her candy after her nap anymore. Have several types of fruit or vegetables (carrot, celery sticks) that you know she likes on hand and have her choose one. If she objects, in a matter-of-fact manner, say "Well, I guess you don't want a treat after your nap." Stick to your guns. It's worth it. It's also definitely advisable to eliminate all candy except for special occasions, just by letting her choose a healthy substitute. She may not even blink an eye. Concentrated sugar can be "addictive", but if you stop buying it, you'll have an easier time breaking the habit. Another suggestion: if you think she's old enough for an "experiment". buy five or six in-season fruits, cut several small pieces of each one when she's not looking, and do a blindfolded taste test to let her decide which one is the absolutely most delicious. Make a game of it.
Another observation: children generally eat the amount of food they need and then stop. Perhaps she doesn't clean her plate because she is full. Try serving her half as much, and if she eats it all and asks for more, you can always give it to her. Her stomach is still small, and so she might need to eat more often. If this works for you, then the candy bribe becomes unnecessary.
I have two grown daughters, both of whom had erratic eating patterns. I tried to go with the flow, offer them nutritious meals and snacks, and let them figure it out. They didn't starve. I also have a family dental practice in Cupertino, so the candy issue is a big one for me. Can you tell? D. Cotner