When you want to find a specific data field, the easiest way is to check the TRTH Data Dictionary. Open tab "Field Descriptions", and use a text filter on column D or E to display only the rows that "contain" a keyword that defines what you are looking for.
I did this for you, but could not find anything related to market capitalization.
I then tried the same thing with the DSS Data Content Guide. DSS is a product similar to TRTH, both use the same servers, but have slightly different purposes, and different commercials. I'm including this information here because sometimes people confuse DSS and TRTH. Also, some customers have both products as well, maybe that's your case ? With DSS, filtering column D on "Market Cap", the attached screenshot shows there are 5 fields relate to market capitalization, split over 2 templates (i.e. API calls).
I conclude from this that market capitalization is available to DSS customers but not TRTH customers. If you have DSS you can check out REST Tutorial 3 on Intraday Pricing, and REST Tutorial 8 on Composite data extraction for details on the required calls.
Caveat: this forum is for software developers using Refinitiv APIs, and technical discussions. The moderators on this forum do not have the required deep expertise in all the content sets available through our products to answer such questions with certainty. For precise data queries, and to ensure there is no other solution for your specific query, please directly contact TRTH support team via MyRefinitiv. In the product field, select "Thomson Reuters Tick History v2".