The 1841 Census has
Anthony, William, 45, Shoemaker
Antony, Phoeby, 40
Anthony, William, 10
Anthony, Mary, 8
Anthony, Margaret, 5
Anthony, Ann, 15
Address Cythir, Kidwelly (transcribed as Kitter), all born in County (Carm)
1851 has
William, 57, Shoemaker, born Kidwelly Borough
Phoebe, 53, born Llangendrine (as transcribed)
Margaret, 14, born Kidwelly
Address Cythir, Kidwelly
Might be your Anthony although there is another William Anthony, born Llanarthne 1795 - a shoemaker also.
regards