Interesting question. Most of the time, you can use either word. But notice that "expert" can be used as an adjective or as a noun. If you are using it as a noun, I think it sounds better to use "in": "He is an expert in computer programming". But, "at" wouldn't be wrong. "In" just sounds better to me. If you are using it as an adjective, you don't need either word: "He is an expert computer programmer." But, as an adjective, "at" is preferable (to me, at least) to "in": "He is expert at computer programming". But, "in" wouldn't be wrong. "At" just sounds better to me. All in all, this isn't an issue you need to worry about much.

He is an expert at making trouble. Meaning he is very good at causing trouble. I am an expert in making cakes. - She does it very well. She is an expert in horse riding. He is an expert at playing cards. Hope that helps. Kat the teacher