Which is better, being overqualified or underqualified?

With all these jobs out there, is there any way to underqualify yourself if someone were to say you're overqualified? I don't want to reduce or increase the years of research experience I have under my belt, otherwise, I would see myself as a fraud. For some positions that require up to 10 yrs of experience, what type of person are they looking for? Thanks in advance.

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