Short answer: you can't.
Little longer answer: If you know what you are doing you can always reverse engineer a given application and use its api. You can only make it more difficult and time consuming, using authentification via tokens and device ids or usernames is a good first step. Apart from that: why would you want to close your api to outsiders? If your server code is written well there is nothing to worry about.
You can maybe secure your API on a legal basis and sue developers who use it, but that is a completely different topic.
Some clarification regarding securing the API and securing content via the API. Assume you create a server where you can send user/password and receive a token if that combination was correct. For the account-page you send said token over and the server verifys that that token is valid and returns your account page. You secured the actual content of the API. That is obviously very possible and almost a must-have unless you have no user-specific data. But still everybody can send the exact same initial request from their custom app, sending a user/pass and again receive a token, etc. You cannot really prevent the request itself or even determine that it was not send by some service not authorized by you. You can send some hashes along the request to add some security by obfuscation, but since your app has to compute them, so can the reverse engineer.