If you can use Carbon then this code will work fine for you.
$dateS = new Carbon('first day of January 2016');
$dateE = new Carbon('first day of November 2016');
$result = ModelName::whereBetween('created_at', [$dateS->format('Y-m-d')." 00:00:00", $dateE->format('Y-m-d')." 23:59:59"])->get();
Or you can check the issue by debugging query using DB::enableQueryLog();
and DB::getQueryLog();
functions like
DB::enableQueryLog();
$dateS = new Carbon('first day of January 2016');
$dateE = new Carbon('first day of November 2016');
$result = ModelName::whereBetween('created_at', [$dateS->format('Y-m-d')." 00:00:00", $dateE->format('Y-m-d')." 23:59:59"])->get();
var_dump($result, DB::getQueryLog());
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