If I got you correctly, then here is your solution:
1. Fist open the file “post_retrive_ajax.php“ from the plugin folder a-to-z-category-listing.
2. Go to line number 86. Here you will find a line like:
$psql = ” select * from “.$table_prefix.”posts wpp,”.$table_prefix.”term_relationships wpr where wpr.term_taxonomy_id = ‘$ttid’ and wpr.object_id = wpp.ID and wpp.post_status = ‘publish’ and wpp.post_type = ‘post’”
3. Now add the following code to the end of the line.
order by wpp.post_date DESC
That means the line will be :
$psql = "select * from ".$table_prefix."posts wpp,".$table_prefix."term_relationships wpr where wpr.term_taxonomy_id = '$ttid' and wpr.object_id = wpp.ID and wpp.post_status = 'publish' and wpp.post_type = 'post' order by wpp.post_date DESC";
Do the Same for the line 147:
Add the following code to the end of the line(no. 147).
order by wpp.post_date DESC
That means the line will be:
$psql = "select ID,post_title from ".$table_prefix."posts wpp,".$table_prefix."term_relationships wpr where wpr.term_taxonomy_id = '$ttid' and wpr.object_id = wpp.ID and wpp.post_status = 'publish' and wpp.post_type = 'post' order by wpp.post_date DESC";