From Samuel Lewis's Topographical Dictionary of England, 1849 (pp. 238)

FISHBOURN (sic), NEW (St. Peter and St. Mary), a parish, in the union of WEST HAMPNETT, hundred of BOX and STOCKBRIDGE, rape of CHICHESTER, W. division of Sussex. 1¼ mile (W.) from CHICHESTER; containing 295 inhabitants. It is bounded on the west by Chichester harbour. The living is a rectory, valued in the king's books at £5. 10., and in the patronage of the Crown: the tithes have been commuted for £176. 16.; the glebe comprises 14 acres, and the Dean and Chapter of Chichester receive a sum of £10. 14. per annum. The church is in the early English style. The remains of a Roman bath with a tessellated pavement were discovered in 1812 near the site of the Roman road here.