I would like to apply for a postdoc position or an academic position like an assistant professor. Before I had three persons who could write letters of recommendation for me in case I needed to apply for a job. Unfortunately I had a conflict with one of these persons who wrote a letter for me and he/she has decided to not to write a recommendation letter for me anymore. I am left with only two people who can write letters for me. Since most of job applications require at least three reference letters, I do not know where to find the third person to write the letter for me. Any suggestion? If I submit my application with only two letters, will it be rejected as incomplete? Is it a bad sign if I send only two letters in those cases where are requested at least three or more?
If I submit my application with only two letters, will it be rejected as incomplete?
Yes, probably. That is what the word "required" means. It is possible that some employers might consider the application anyway, or perhaps give you more time to submit a third one, but many will not.
They want to make sure they are getting a range of opinions on the candidate's qualifications, to reduce the chance that they are just hearing from one or two biased people writing inaccurate letters.
Is it a bad sign if I send only two letters in those cases where are requested at least three or more?
So you should try harder to find a third person to write a letter. We have lots of questions on this site about how to find letter writers. For instance, you can tell your other two writers about the situation, and ask if they have any ideas.