Ms. Fleming, an attorney from Noyac who also ran on the Independence line, will fill the council seat vacated by Supervisor Anna Throne-Holst when she became supervisor in January.
The Republicans now have a 3-2 advantage on the Town Board. Ms. Throne-Holst was elected on the Democratic line but she is not registered with any political party.
Mr. Hughes is a Southampton Town Police lieutenant who retired this month.