Native mobile app development is different for each and every Operating System. That is why, instead of focusing on one particular platform, we decided to give relevant access to the correct guides.
iOS
Apple goes through a brief introduction to their different accessibility tools, such as VoiceOver and Guided Access. They also feature more than half a dozen of videos of Apple Engineers talking about iOS accessibility, recorded at their previous WWDC events. Also available is a series of article going through specific UIAccessibility protocols and their important "Accessibility Programming Guide for iOS".
Android
The Android accessibility guide features several articles teaching you about the best practices for building an app for the Google-owned OS. They go through certain requirements and recommendations, as well as special considerations. Also available are tips for debugging and details about accessibility events.
Windows Phone
Microsoft offers an overview of the concepts and technologies associated to the Universal Windows Platform apps, which allows you to develop accessible apps for Windows 10 as well. Their guide is pretty complete and in-depth, as they go through best practices, accessibility testing and different code exemples for different scenarios.