How to reference a specific field?
Technically, you could add a reference field to field config entities. But you can't limit the options there and I'm sure you don't want to allow all the fields, and you need custom theming logic for this anyway. That would just allow you to select the field name.

You can't link to a field value, the combination of entity and field doesn't have its own identifier.

If I understand you correctly, then the simplest option is to make a custom list field with allowed values like this:

field_name_a|Field A
field_name_b|Field B

With as many fields as you need. You could also register a allowed options callback and try to dynamically limit the options based the current page/node type, but that's a bit tricky.

Then you need custom logic in preprocess/twig templates for that paragraph type that gets the value for the selected field from the parent of the paragraph and renders it