Shabbos Daf 135 שבת דַף 135

The Gemara brings a Baraisa that teaches that the word ערלתו - his foreskin, is coming to exclude several cases in which performing milah on Shabbos is not permitted. One of the cases is one who is born מהול - circumcised.

The Baraisa states that Beis Shammai holds that one who is born mahul still requires הטפת דם - the drawing of blood, whereas Beis Hillel does not. Rashi explains that Beis Shammai requires  הטפת דם because perhaps the baby has an ערלה כבושה - a suppressed orlah.

Rebbe Shimon ben Elazar says that Beis Shammai and Beis Hillel agree that a child born mohel requires הטפת הדם. They disagree in a case of a ger, who converted when he was already circumcised. Beis Shammai requires hatafas dam, and Beis Hill does not.  In this case there is no concern of an ערלה כבושה. The הטפת דם here represents a symbolic act of entering the bris .

Rebbe Assi stated a rule, כל שאמו טמאה לידה נימול לשמונה – Any newborn whose mother becomes tamei due to childbirth, is circumcised on the eighth day, וכל שאין אמו טמאה לידה אין נמול לשמנה - while any newborn whose mother does not become tamei due to childbirth, (for example a woman who had a caesarean birth), is not circumcised on the eighth day, but rather on the first day. He learns it from the juxtaposition of the passukאשה כי תזריע וילדה זכר וטמאה   - When a woman conceives and gives birth to a male, she shall be tamei, with the passuk וביום השמיני ימול בשר ערלתו - and on the eighth day, the flesh of his foreskin shall be circumcised.

A Baraisa is brought that discusses when the milah for a baby  עבד כנעני is performed, and distinguishes between a  יליד בית, a child born to a shifchah who is the property of a Jewish master, and a  מקנה כסף, a slave that was purchased.  According to the Tanna Kamma:

Rav Chama disagrees and has a different understanding of these four cases.