If you are still unable to understand a proposed layer pattern, simply do not use it. It's no use just putting N layers if you do not understand why each one exists.
There's a KISS concept (Keep it simple, stupid), I'm not calling anyone stupid, it's the concept. Translating is keep it simple. Watch this talk by a StackOverlflow employee, it's in Portuguese. You will see the simplicity behind this site. Simplicity often caters.
In most cases the simple MVC pattern that comes by default in an ASP.NET solution will suit. In your case of an API, you will not have the Views, but you would not need to create layers unless it is extremely necessary, and if you can not identify if it is necessary, then do not.
Focus on delivering functionality to the client securely and well, at least by following the basic principles of object-orientation such as separation of responsibility and #.
Take this pattern of layers, and try to develop something for testing, so you can learn and understand, but do not do something that will be sold or put into production with something you do not master.