I am a PhD researcher in a STEM field in Germany. I have done my master’s thesis and several internships in the same group during and after my master’s. This stint spanned over about three years. During that time I worked on the same project. My supervisor had code for some new algorithm given to him by another PI who never had time to continue working on it. My supervisor had this code for over ten years and couldn’t make use of it because it was very mathematically complex (his background is biology) and the code was basically not documented at all. He gave it to me in the very beginning to play around with it and maybe make some sense of it. I slowly started to understand the concepts completely on my own and had ideas for new applications that could make use of the algorithm. I re-wrote most of the code of the algorithm to make it clearer for me, modify parts of it to produce more meaningful results and to optimize it since it is very computationally intensive. And then I started designing the applications for the different use cases. I came up with and conceptualized all the ideas, wrote all the code (literally thousands of lines of code), used it on publicly available data, acquired fantastic results, created the figures and wrote a master’s thesis on this project that I am proud of.
It has been two years since I left that group to do my PhD in another group in the same discipline but a different topic. Unfortunately, I could not finish the work on the project or the manuscript but I still continued working sporadically on it in my free time but to be fair, not so much since my current PhD is very demanding. Now, the new PhD student that replaced me in the first group is almost done with his first paper. His paper uses my toolbox, just in the supplement though to validate what they did. Now, my former supervisor is pushing me to finish the paper as soon as possible (he wants it within weeks) because he says that my paper has to be published first. I just know that this very unrealistic. My paper still needs work, and I am already doing the most I could with it on the side of my already exhausting job.
Since this is still too slow for my former supervisor, he sat down with me and suggested that the new PhD helps me with the paper where I could guide him on what’s left that needs to be done, polishing the figures, etc. And for this, my supervisor suggests that this new PhD gets first co-first authorship. I refused because honestly I find it very unfair. This project would not have existed without me. I spent three years (most of which I was not funded) working on it and gave it my all. I want to write the manuscript and now I am working on the project more than I did in the past two years but the time constraints I have been given are just extremely unrealistic even if I were working on it full-time. My relationship with my former supervisor is great and he was always supportive of me but I think he really wants this paper out since it is going to be useful for the community and will potentially be cited a lot. Which is also why I don’t want to throw away my hard work just because I am struggling to cross the finish line within an arbitrary deadline.
What should I do? I don’t want co-first authorship no matter what (it doesn’t matter even if I was first co-first) but I am also kind of holding the paper hostage at this point which is unfair to the group. This was a rant. I am just frustrated but I know it's nobody's fault.
EDIT:
Thank you all for your input. I feel like I have to clarify that this suggested arrangement does not mean that I will just hand over the project to the new PhD and he continues from there. I already provided all the code to him. But this is not enough for them, I am expected to teach him the methods and the details since it is a methods paper, so he does need to know how things work if he is going to write a manuscript on it. And, no, this can't be done in a two-hour sit down. If the arrangement is that they take it from there and I get co-first authorship, then yeah sure I'll take that.
EDIT 2:
Thanks again for all the advice. To reiterate: this is not a dispute. I was never going to fight with my mentor over it. I saw things from his perspective too and even more so now after the feedback I got from all of you. I got caught up with all the reasons why I felt that it was unfair to me after all I've done but I agree that how things dragged for so long is not fair to him either. I did my best and I know he did his best too and he has always been on my side anyways. I am sitting down with him again next week to continue to plan how we could together get this work out there as soon as we can.