I have 16 examples in my collection of this coin in various dates from 1907-1928, and I don't see anything that leads me to believe your example is fake. 1924 is the most common date (followed by 1928 and 1908NM). In other words, if someone was planning to counterfeit a Saint using real gold, counterfeiting the most common date would make little sense as there is unlikely much numismatic value beyond gold melt value.
As others have said, weight, diameter measurement, ring and (if you have the capability) spectroscopy are ways to better assure yourself of authenticity.
Edited by usc96
08/21/2021 11:22 pm