6. Who to circumcise:[1]

Androgenus:[2] An Androgenus is to be circumcised [without a blessing].

Two foreskins or two Gidim:[3] A child born with two foreskins[4] or two complete sets of Gidim is to be circumcised.

C-section/Caesarean:[5] A child who was born Caesarean is to be circumcised.

Ben Mumar:[6] A child born from a father who is an apostate Jew[7] is to be circumcised.

Mother Jewish, father not:[8] A child born from a gentile father is to be circumcised.

Father Jewish, mother not:[9] A child whose mother is not Jewish is not to be circumcised, just as we rule regarding a non-Jewish child, as explained in Halacha 9.

[1] See Michaber Y.D. 262:3; Pesakim Uteshuvos 262:14; See Encyclopedia Talmudit Vol. 46 Erech Mila p. 425-427 footnotes 251-262

[2] Admur 331:6; Michaber Y.D. 262:3; 266:10

An Androgenus is a person born with the both the male and female genitals. See Pesakim Uteshuvos 262:14 footnotes 108-111

[3] Admur 331:6; Michaber Y.D. 266:10; Shabbos 135; See Michaber Y.D. 262:3; Pesakim Uteshuvos 262:14 footnotes 112-113

[4] Two foreskins, one over the other.

[5] Admur 331:6; Michaber O.C. 331:5; Y.D. 262:3; 266:10; Shabbos 135; Shevach Habris 8:3; See Os Chaim Veshalom 266:8

[6] Michaber Yoreh Deah 266:12

[7] Known as a Mumar.

[8] See Pischeiy Teshuvah Yoreh Deah 266:14

[9] Michaber Yoreh Deah 266:13