Sharepoint - Can I sort my sites using their Title inside my content search web part
The title of a site (the one present on (/_layouts/15/prjsetng.aspx page) resides in a crawled property called ows_SiteName.
You should map it to a RefinableStringxx managed property(see below screen grab) and then click OK.
To do that, go to your Central admin > Manage service applications > Search service application > Search Schema (under queries and results)
Once the mapping is done, do a full crawl of the data source.
After that, you will be able to sort the results based on the site's title property.
You probably can also use another search mapped property called "SiteTitle", no need to create any extra refinableString then ;)
You can map title to one of the RefinableString, crawl, and sort by that RefinableString
UPDATE
Go to Central admin > Manage service applications > Search service application > Search Schema (under queries and results)
Find one RefinableString (for ex RefinableString00,RefinableString01...), edit property and add one of titles.
You can add ows_SiteName or one of the Title managed property (for ex. Basic:displayTitle).
After that you have to recrawl (full crawl).
Then edit your wp and add sorting by RefinableString00
SORTING
Not so many predefined managed properties are sortable, maybe because MS implemented FAST Search with default sortable properties in SP2013.
You could also edit SiteTitle (ows_SiteName managed property) on CA > Manage service applications > Search service application > Search Schema.
Change sortable to Yes-active and recrawl.
On SPO you can't do that, only map to Refinable managed property
Link
Sorting has always been a big deal and highly requested feature in previous versions of SharePoint. You really couldn’t sort by many criteria at all without writing custom code. In SharePoint 2010, FAST Search for SharePoint added sorting capabilities but many people didn’t care to pay for it. Well, now sorting is a first class feature in SharePoint 2013. You can mark managed properties as sortable now and then use them in the search results web part. Note, that you can only do this for properties at the Service Application level.
EDIT 2
You could create new Result Source which would override your sorting on wp.
Go to Site settings>Site Collection Administration>Manage Result Sources Create new, give it name like Sort Site Title, under Query Transform Launch Query Builder and add sorting to your RefinableStringXX ASC.
Edit your CSWP (Content Search Web Part) and select your new result source under Select a query
link