As stated, this is a complex question. During exercise you are burning some of both sources and even some from protein. The amount depends on a number of factors. All of these factors play a different role in the energy system at different times. In a nut shell, fat takes a longer time to contribute energy and tends to be too slow to contribute in high intensity exercise the way that carbohydrates can. But fat does still contribute in all exercise to some degree.
If you are looking at this from a weight loss perspective, fat will contribute to the recovery refueling of muscle energy stores after exercise along with the post exercise fuel that you should be consuming. The body will allocate calories to go back into the fat cells if there is enough excess to cover it. Some of the fat energy is going to go into the fat cells no matter what, but if there is a calorie deficit (not too extreme), the fat cell will release some of that restored fat over the course of time.
I have really (really really) over simplified this as I don’t think I should spoon feed you everything. I do teach such topics to interested students. And this type of information is the type that I do feel can be shared in an online learning environment. You can check out my website if you think you might be interested in some of my CEC courses. I teach over a dozen topics that are already set up. But I also teach to specific request topics as needed. www.hawaiifitnessacademy.com or contact me through my IDEA profile.