The place to look is the Metadata API Developer Guide, in the Metadata Types section.
Note on terminology: these are not Custom Metadata Types. Custom Metadata Types are a specific Metadata API entity. CustomObject, for example, is a built-in Metadata API entity.
I'm not aware of such an API, or any other way of extending standard metadata like this. I think you might be forced into:
Storing the values you require as some Custom Metadata Type, with a 'Key' field that holds the Object and Field API names for querying.
Storing the values in some global utility class, with each JSON string being a value in a Map of <...