N'cai was a planet located in Federation space in Sector 78 of the galaxy's Alpha or Beta Quadrant.
History
In 2270, the starship USS Enterprise was assigned to investigate an armed, unidentified, unmanned vessel that had been reported in Sector 78. On stardate 6013.4, the Enterprise was near or orbiting N'cai.
Three months later, a temporal disruption threw the Enterprise back to stardate 6013.4, but to a different location. Starbase 7's long-range scanners showed that the Enterprise in Sector 78 had now vanished. (TOS - Mudd's Angels short story: "The Business, As Usual, During Altercations")