How to select year and month from the created_at attributes of database table in laravel 5.1?

There are date helpers available in the query builder:

$post = Mjblog::whereYear('created_at', '=', $year)
              ->whereMonth('created_at', '=', $month)
              ->get();

If you want to get the year and month from a single instance of Mjblog you can access them like this:

$year = $post->created_at->year;
$month = $post->created_at->month;

Read more about Carbon\Carbon getters documentation.