I'm required to include a biography at the end of a journal article written by myself, John Doe, and my supervisor, John Smith. I'm a BSc candidate in Information Systems Engineering at Piled Higher and Deeper, where my supervisor is Research Director. My supervisor is also a Lecturer at Another University. How should I present that information in the biography?
The following answers the original question, not the edited question. I'll update if the OP confirms they're satisfied with the edit.
Questions about the English language are off-topic here, but the question might be on-topic had the context been explained. E.g., in a journal article's biography, how should the authors' titles, affiliation, etc. appear. In that context, for the examples given, I suggest:
John Doe, BSc candidate, Subject Name, University A.
(It's unclear from the question what the precise Subject Name is.)
John Smith, Research Director, University B, and Lecturer, University C.
Since the full addresses of Universities A-C presumably already appear elsewhere, e.g., as author affiliations, they can be omitted.
John Doe, BSc candidate. John Smith, Research Director and Lecturer.
(Options are numerous.)