You should define a CommentController with an index method that takes a post as an argument. By leveraging route model binding you can have instant access to the post model object and then access the comments from a relationship defined within the post model (You said you know how to go about this so I wont dwell on it).
The setup will then be as follows;
routes file (api.php)
Route::get('/api/post/{post}/comments', 'CommentController@index');
CommentController.php (index method)
public function index (Post $post)
{
$comments = $post->comments;
if (request()->wantsJson()) {
return response()->json($comments);
}
return view('your_view_file', compact('comments'));
}
Assuming you are using the same controller for the API and Web business logic, you can use the condition indicated to return json data for APIs or proceed with loading a view for web apps.