Brit mila on Shabbos when father is non Jew
brit mila on Shabbos
Does everyone agree that a brit is done on Shabbat even if the father is a goy?
No, this is a dispute among the achronim [halachic authorities of the last 500 years]. The halachic ruling is that we do in fact perform the bris mila on Shabbos.
See Derisha Y:D 266:20, Nachalas Shiva [kuntress hamila siman 1], Shu”t Binyan Tzion [Vol. 1:21].