First of all, you need to add the new field in the sidebar list  – you do that in wpresidence/templates/directory_filters.php 
The actual search is made via Ajax
The js events are in wpresidence/js/property_directory_control.js. 
Add your event (click/change) and call function wpestate_directory_filtering_action in the same file
In that function read the new field and send it via ajax call to the PHP function wpestate_classic_ondemand_directory .
This function is located in wpresidence/libs/ajax_functions.php ,  and in there you need to retrieve the new field and use it in the Wp_Query arguments.
If your field is a taxonomy follow the example for property status – the $status_array that is added into ‘tax_query’  parameter
If your field is a meta value follow the example for property_size . See how size array is build and added into $meta_query array. Also please note that on property_size  we do a “”Between” search.