Hi,
Once you create a custom Description for example named "MyDescriptions" in a library, input some data for test.
And then do a full search crawl, Search Service Application will automatically create the crawled property named "ows_fieldname":


Now, you could create a new Managed Property and mapping to this crawled property and make the managed metadata searchable:


Finally, this managed property could be used in your search query and return search results.
Reference:
https://www.techmikael.com/2014/07/what-makes-sharepoint-column-searchable.html
Thanks
Best Regards
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