Try
[!AjaxSearch? &liveSearch=`1` &parents=`32,33,34,35` &depth=`1` &jscript=`jquery` &jsJquery=`assets/js/jquery-1.3.2.min.js` &whereSearch=`content:null` &withTvs=`yourTvName` !]
By using &whereSearch=`content:null`, you exclude the search in document fields
By adding &withTvs=`yourTvName` you search only in the tv named 'yourTvName'
And if needed, rather to use @FILE:assets/snippets/ajaxSearch/templates/ ... for each template, try to use chunks.
And obviously, remove the debug mode in production.