I have no experience with Adobe Sign and Mendix (or at all) but I am working on something similar using DocuSign. Mendix has created a module for DocuSign, which can also be embedded in the application. DocuSign is API driven and thus this can be fairly easily implemented in your application. I don’t know if this is also true for Adobe. You could check the Mendix DocuSign Connector module (Mendix Marketplace - DocuSign Connector) and the DocuSign documentation for some inspiration (https://developers.docusign.com/esign-rest-api)
You can achieve this using several services including HelloSign or Docusign. The feature you’re looking for is called “embedded signing”.
Walkthrough example developers.hellosign.com/docs/embedded-signing/walkthrough/