Applying for a postdoc. Should I mention that I completed my PhD with no supervision?
Should I mention that I completed my Ph.D. with no supervision?


Definitely not.  "I had no supervision during my PhD." could be interpreted as "Nobody taught me anything during my Ph.D. so I am unqualified." or "I am incapable of giving credit to other people who deserve it." or "I am so obnoxious my supervisor will not interact with me." or "I refuse to work with others."  It is likely none of these are true, but the misinterpretation is a possibility.

What should happen is that your supervisor writes a letter of recommendation saying that you have shown a high degree of independence and that you now have more expertise in Y than they do.