The Galileo gambit is a cognitive bias (rather than an actual logical fallacy) where the putative expert insists that he is an unacknowledged genius, a maverick who is shunned by mainstream science because of his unconventional ideas. It is similar to the Dunning-Kruger cognitive bias.
The argument is based on Galileo, who was ridiculed in his time for his scientific observations. However, he was later acknowledged to be right. The proponent of this fallacy argues that since their non-mainstream views are provoking ridicule and rejection from other scientists, they will later be recognized as correct, like Galileo.
Of course, comparing oneself to Galileo takes a certain amount of chutzpah. And, Galileo supported his ideas with scientific evidence that was dismissed by unscientific religious leaders.
Example of the Galileo gambit
They claim to be an expert in vaccines because they have a Masters of Public Health, but their radical ideas have been rejected by mainstream medicine because Big Pharma and the CDC are suppressing their ideas. They believe that their knowledge will eventually be shown to disrupt all of our dogma about vaccines.