Some fonts do not appear correctly on mapped domains.  I suggest that you select a font that does appear correctly in the domain. 

Google Fonts are served as web fonts as part of every Google Sites page. 

Google Sites also allows site editors to select additional fonts, also available in Google Docs and Slides, even if not listed in Google Fonts. These fonts are licensed to Google for use on Google’s domains, but do not work with custom URLs. 


At site editor

At domain