getting the current user entries from elementapi
If you really want the entries for the currently logged in user, having a parameter for userId in your endpoint URL doesn't really make sense.

Not tested, but something like this should work:

'api/v1/user.json' =&gt; function () {

    $author = craft()-&gt;userSession-&gt;getUser();

    if (!$author) {
        HeaderHelper::setHeader(array('status' =&gt; 404));
        craft()-&gt;end();
    }

    return [
        'elementType' =&gt; ElementType::Entry,
        'criteria' =&gt; [
            'section' =&gt; 'jobs',
            'authorId' =&gt; $author-&gt;id,
        ],
    ];
}


Notice that the above example endpoint would be available at http://example.com/api/v1/user.json, where your example code would create an endpoint with a required userId parameter, i.e. http://example.com/api/v1/user/12345.json.

Also notice that the currently logged in user is pulled via the UserSessionService (craft()-&gt;userSession). 

Finally, note that you should use 'authorId' =&gt; $author-&gt;id in your criteria – not 'author' =&gt; $author.