The Normandy class of starfighters were a type of auxiliary craft in service to the Earth Starfleet, ca. 2160. (date adapted from Star Trek Spaceflight Chronology)

Fighters of this class replaced the veteran Arrow-class and Galliant-class starfighters that saw heavy combat during the Earth-Romulan War. (FASA RPG: The Romulan War)

As the United Federation of Planets was founded shortly after the end of the Earth-Romulan War, these were probably in service to the nascent Federation Starfleet as well. Despite Star Trek Spaceflight Chronology's assertions that the fighters had "advanced second generation warp drive," they could not have been warp-capable, given the technology level of the era. It is possible, however, that the fighters had some kind of one-use only emergency fusion-powered low-yield drive.
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