It seems every postdoc position needs representative papers. What should I do if I don't have any publications?
Your question is very much field dependent. In some fields it is acceptable to go without a single publication for your PhD (I believe this is true for some subfields in economics, literature and math). However, you are expected to produce according to your community's standards: for example, in the economics/maths examples above you are expected to have at least one or two working papers/papers under submission containing solid results that were discussed in some workshops. In the literature domain, I understand that there's a lot of focus on teaching, written essays and book reviews etc. (I get this knowledge secondhand, I'm far from a humanities faculty). In my field (CS/AI/ML) you wouldn't be allowed to graduate with one average publication, and would most likely not have been allowed to go 4+ years into your thesis, unless there were very unusual circumstances (you mention industry, so I'm assuming you are at the very least in a STEM discipline).

So, the question you should be asking yourself is: am I comparable to my peers in terms of my PhD accomplishments?

If you have a lot of amazing work that just needs a bit more time, you can either


Ask your advisor to graduate in another year to let these results come to fruition under the umbrella of your thesis OR
Put them up on ArXiv (or the equivalent) and list them there. This is not ideal, but at least it shows that you weren't idle.


From the perspective of a postdoc host, I would most likely pass on an application that's clearly lacking in publications, even if it is backed up by glowing references. I would be more inclined to accept one that is backed up by preprints, if they contained amazing results that are vouched for by people whose opinion I respect. Postdocs should be people who are able to support their own research thread without very close supervision (they should be more independent than grad students at the very least), so you should prove to me that this is indeed the case; this is a tall order without proof that you can actually publish peer-reviewed work in good venues on your own.

I'm sorry to offer an answer you most likely don't want to hear, and I wish you all the best!