Fetch year-wise month list if have posts in particular month in WordPress

month_list.php

<?php
global $wpdb;
$query = "select date_format(post_date, '%Y-%b') as yearmonth
          from ".$wpdb->prefix."posts
          where post_type='post' and post_status='publish'
          group by yearmonth
          order by yearmonth DESC";

$result = $wpdb->get_results( $query );

$final_array = array();
foreach( $result as $row )
{
    $yearmonth = explode( "-", $row->yearmonth );

    $year = $yearmonth[0];
    $month = $yearmonth[1];

    $month_list = array(
                "Jan" => false,
                "Feb" => false,
                "Mar" => false,
                "Apr" => false,
                "May" => false,
                "Jun" => false,
                "Jul" => false,
                "Aug" => false,
                "Sep" => false,
                "Oct" => false,
                "Nov" => false,
                "Dec" => false,
            );

    if( !array_key_exists( $year, $final_array ) )
    {
        $final_array[$year] = $month_list;
    }
    $final_array[$year][$month] = true;
}

// OutPut
echo "<pre>";
print_r($final_array);
echo "</pre>";

Array
(
    [2020] => Array
        (
            [Jan] => 1
            [Feb] => 1
            [Mar] => 
            [Apr] => 
            [May] => 
            [Jun] => 
            [Jul] => 
            [Aug] => 
            [Sep] => 
            [Oct] => 1
            [Nov] => 1
            [Dec] => 
        )

    [2019] => Array
        (
            [Jan] => 
            [Feb] => 
            [Mar] => 
            [Apr] => 
            [May] => 
            [Jun] => 
            [Jul] => 
            [Aug] => 
            [Sep] => 1
            [Oct] => 
            [Nov] => 
            [Dec] => 
        )

    [2018] => Array
        (
            [Jan] => 
            [Feb] => 
            [Mar] => 
            [Apr] => 
            [May] => 
            [Jun] => 
            [Jul] => 
            [Aug] => 1
            [Sep] => 
            [Oct] => 
            [Nov] => 
            [Dec] => 
        )

    [2015] => Array
        (
            [Jan] => 
            [Feb] => 
            [Mar] => 
            [Apr] => 1
            [May] => 
            [Jun] => 
            [Jul] => 
            [Aug] => 
            [Sep] => 
            [Oct] => 
            [Nov] => 
            [Dec] => 
        )
)
?>