The study began in October 2023 and was prolonged to the end of June.
It will now be in place until the end of September.
The price decrease reduces rush-hour trips between Glasgow and Edinburgh by nearly half, from £28.90 to £14.90.
First Minister John Swinney made the news on Thursday while attending a Fife Expo at Edinburgh’s Waverley Station as part of the Levenmouth rail link inauguration celebrations.
He stated, “We know that new rail investment can provide genuine opportunities for education, business, and tourism, as well as serve to revitalize neighborhoods. This is most visible with the soon-to-open £116 million.