The Indian Princess Head $3 gold coin series was produced from 1854 to 1889, and each year typically saw limited mintages. However, the 1870-S issue specifically is not recognized as having been minted.
Consider reaching out to professional grading services and reputable coin dealers or auction houses for a thorough evaluation.
If such a coin were to exist, it would likely be an extraordinary numismatic discovery, and its uniqueness could contribute significantly to its rarity and value.
It's important to stay updated with the latest numismatic research, publications, and auction records, as the field is dynamic and new discoveries can reshape our understanding of coinage history.
If there have been developments or new findings since my last update, checking with current numismatic sources is advisable.