fishdan Jsonmaker lets administrators curate a nested tree of links directly on the front end. Drop the <code>[jsonmaker]</code> shortcode onto a page, expand nodes to add children, rename or remove items inline, and fetch any branch at <code>/json/<slug>.json</code>.
Highlights
<ul>
<li>Inline “Add”, “Edit”, and “Delete” controls for administrators (capability <code>jsonmaker_manage</code>).</li>
<li>Clean JSON endpoint for each node (<code>/json/<slug>.json</code>).</li>
<li>Store either URLs or plain text values; an empty value keeps a node as a container.</li>
<li>All data persists in a single WordPress option—no custom tables.</li>
</ul>

fishdan Jsonmaker

Manage hierarchical link collections via a shortcode, edit them inline, and expose any node as JSON.

dphiffer

GoodBarber

GoodBarber plugin is a fork of JSON API created by dphiffer. 
GoodBarber plugin creates a communication interface between your WordPress and your GoodBarber account. 
It is used to retrieve content from your WordPress so that you can sync it with your native app created with GoodBarber.

GoodBarber plugin allows you to retrieve WordPress content in order to create a native app for iOS and/or Android

fishdan Jsonmaker vs GoodBarber