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Dear Ms. Quintana,
Thank you for posting your request on History Hub!
We searched online and located a website titled “The Genealogy of Mexico: Gateway to the Past from our Ancestors Forward” that has lists of people that it states served with Cortes and stayed in Mexico. Francisco Quintana and Hernando de Quintana are listed on this page. We are not familiar with the creators of the website and can not vouch for its accuracy or completeness, however you may find it useful. The website provides information about the books it uses as sources and other resources on the topic of Mexican genealogy.
The Library of Congress has a number of items in its collection relating to the early exploration and conquest of the Americas, some of which are featured in their online exhibit Exploring the Early Americas: Cortés and the Aztecs. The Library of Congress also has copies or publications of some documents from Cortez such as Cartas y relaciones de Hernán Cortés al emperador Carlos V. We recommend that you contact them via their Ask a Librarian form to inquire about their holdings.
You also may wish to contact the National Library of Spain, the Archives Department of the Spanish Ministry of Culture, The National Library of Mexico, and the General Archive of the Nation [Mexico]. The FamilySearch Wiki page on Mexco Genealogy may also be useful.
We hope this information is helpful. Best of luck with your family research!