How to prevent the breading residue sticking in chicken fry?
You aren't missing anything, it's completely normal for parts of the breading to come off food while it's frying. This residue will keep cooking, leading to blackened breading bit buildup. 

If pieces of breading are sticking then the answer is to fish them out, you can use a metal strainer to do this, there are strainers designed just for that purpose. You could also buy frying baskets (provided you find ones that fit your pan) and cook your chicken in those, the beauty of them is that when you lift them out you take all of the breading pieces that have fallen off with it. 

If it is smaller particles that are the problem then you can get them out by pouring the oil through a fine mesh strainer. This is a bit slow, so you'd want to build a few extra minutes into your cooking process.