A few months ago, I asked here a question about a student in our group who claimed the authorship in our paper, because he was planning to work on the same problem that we did. I said that I refused to accept the co-authorship the night before the deadline because he did not have any contribution. Two days ago, my advisor sent me a message that the other student is planning to follow up and send a request to the conference committee and claim about our paper. We had a meeting about details with my advisor today. He said, "Let me tell you what will happen, the student will send the request, due to the law, the committee has to ask three professors to talk to all of us, and then it will go nowhere because there is no evidence, but it will be so bad for anyone who has been in this process. To prevent this, add the other student's name to your paper". I tried to refuse but he insisted and said "You did the mistake, until one week before the deadline I didn't know what you are working on. You didn't tell me about your work to keep the number of authors at the minimum and become the supervisor. Now you have to add his name". I said that I wish you told me this when you found out the problem, but you said it is okay at the time. If I knew, I would withdraw the paper, and he said this is not a professional manner to withdraw the paper. I am deeply sure that I did not take EVEN A WORD from that other student and am really sad about the situation, but I cannot lose my advisor for my future positions. But my question: my collaborator (the first author) and I worked on the paper and both proposed the idea and divided the coding into two parts. My collaborator did more than I did in the writing. That is why my collaborator is the first author and I am the second with equal contribution (I was the supervisor who defined the problem). Now, I should add this new student's name, where should I put the new name? Shall I add the new name as the second author to keep my supervision and also the effort? I cannot ask my advisor, because it seems that he wants just to solve this problem without any conflict and doesn't care about my situation.
My field is computer science in medical applications.
Thanks a lot for reading and answering.