An association in Corsica wants to build one
https://www.yacht-concept.fr/uk/wp-content/uploads/sites/2/20-04-Fiche-Chebec-UK-reduced.pdf
A Galeotta : Sciabeccu Chebec Xebek Sciabecco Bastia Corsica https://www.facebook.com/galeottadiBastia/
Are sure you want to build one? It's a task for very qualified classical naval carpenters and needs a shipyard. Even finding the suitable woods will be a pretty difficult task. And I do not talk about cost because it's in millions of euros. We are talking about merchant or warships rather big, pretty heavy thus pretty expensive.
A more reasonable task is to build like Jehardiman said a felucca, or a traditional work boat with latin sail. There are many types in a lot of sizes in the Mediterranean Sea, with a lot of living associations in Spain, France, Greece, and lot of people able to help you.
You have even sail makers knowing these sails for example
Voile latine | Voiles classiques pour vieux gréement | Voilerie https://h-sails.com/fr/voiles-classiques/76-voile-latine.html.
I've joined a PDF in french on the subject edited by the french Ministère de la Culture.
There is a very active association at Sète, a very nice harbor in France VOILE LATINE DE SETE ET DU BASSIN DE THAU
The internet site has plenty of infos and documents
VOILE LATINE DE SETE ET DU BASSIN DE THAU – Chantier naval de la Plagette – Patrimoine Maritime Méditerranéen https://voilelatinesete.org/
To have an idea of the smaller and affordable cousins of the Xebec you can find around France and Spain a link to a page of Pinterest.
https://www.pinterest.fr/pin/436708495127348400/