My App min version is 14393 and target version is 15063. So the question is that do I need 14393 SDK or having only 15063 strong text is sufficient?
You could choose to install only 15063 SDK. Once you only install the 15063 SDK, then your target version could only set 15063 and the min version could be 10240 ~ 15063.
In short, only installing one SDK will not affect you to develop your UWP app, but you need to consider your app's users, their environment was not necessarily the same as yours.
For example, your project's target version is 15063 and min version is 10240, then, you develop and test your app on 15603 OS successfully, but your app can be installed on 14393 OS. In your code, once you call an API that is introduced from 15063, then the app run on 14393 will fail.
The document Choose which version to use for your app mentioned by @Bite has explained this scenario:
The value of Target Version is used to identify all the references (contract winmds) used to compile your project. But those references will enable you to compile your code with calls to APIs that won't necessarily exist on devices that you've declared that you support (via Minimum Version). Therefore, any API that was introduced after Minimum Version will need to be called via adaptive code. For more information about adaptive code, see Version adaptive code.