I want to query posts in monthly basis

First, get the current month and year:

$month = int(current_time('m'));
$year = int(current_time('Y'));

Next, get the posts in this month:

$query = new WP_Query( 'year=" . $year . "&monthnum=' . $month );

If the query returns empty query the month before and repeat this until you have found a non empty month:

while (empty($query)) {
  $month = $month-1;
  if ($month == 0) { $month = 12; $year=$year-1;}
  $query = new WP_Query( 'year=" . $year . "&monthnum=' . $month );
  }