In a case when a non-Jew wishes to convert to Judaism but already has a bris milah, a procedure or process known as "hatafas dam bris" is made. That's where a small needle is put in the place of the bris and a small amount of blood is drawn out.
What is the source for this? What is the purpose of this? And why is it done?
In short, one of the requirements for a male convert is to enter the covenant of Abraham as the Jews did in the desert (after leaving Egypt) from where we learn the requirements of conversion
To enter the covenant of Abraham an action needs to be made (specifically if you were not born jewish) in perfect circumstances the foreskin needs to be removed (preferably the outer skin cut off and the thine inner membrane ripped apart) by someone who is in the covenant already (a jew)
But if there is no foreskin for whatever reason (born like that or it was removed before) then the action of letting blood according to the opinions that we follow for law from that place brings you into the covenant (not only by a convert but also if you are already Jewish and did not yet enter the covenant yet)
R. Joseph said: Whence do I know it? Because it was taught, R. Eliezer ha-Kappar said: Beth Shammai and Beth Hillel do not disagree concerning him who is born circumcised, that one must cause a few drops of the covenant blood to flow from him. Concerning what do they differ? As to whether the Sabbath is desecrated on his account: Beth Shammai maintain, We desecrate the Sabbath on his account; while Beth Hillel rule: We must not desecrate the Sabbath on his account.
גר שבא להתגייר אינו גר עד שימול ויטבול היה נימול כתב ר"ח שאין לו תקנה אבל בניו נימולין ונכנסין בקהל דהא אגייר בטבילה וכגר חשוב להכשיר זרעו אבל לא הוא ובעל הלכות כתב שיש לו תקנה שמטיפין ממנו דם ברית ובעל העיטור כתב שאם נולד מהול א"צ להטיף ממנו דם ברית אלא בטבילה לחוד סגי כאשה ואם לא נולד מהול אלא שלא נימול לשם גירות כגון ערבי מהול צריך להטיף ממנו דם ברית וא"א הרא"ש ז"ל לא חילק אלא בכל ענין צריך להטיף ממנו דם ברית וכתב עוד אם נכרת הגיד אין מילתו מעכבת מלהתגייר וסגי ליה בטבילה וכ"כ גאון סריס שבא להתגייר נכנס תחת כנפי השכינה כאשה...
My translation
A convert that comes to be converted is not converted until he is circumcised and dipped (in a mikva)
if he was already circumcised write Rabbi H' that he can't be fixed (converted) but his children can be circumcised and can join the congregation (I think it means that they are considered as having had a Jewish father) since "a convert that only dipped and did not get circumcised is considered a convert to permit his children but not himself"
(But) The author of the Halochois Gedoilos writes that he can be fixed by taking a drop of circumcision blood
The author of the Itur writes that if he was born circumcised (with out a forskin) we do not need to drip circumcision blood, it is enough (just) to dip him as by a woman, but if he was not born circumcised but he was already circumcised but not to convert I.e. a circumcised Arab (Muslim) you need to drip from him circumcision blood
And (but) my master my father the Rosh zal did not differentiate, it (the law) is just any time (all above cases) you need to drip from him circumcision blood, and he additionally writes, if the organ was cut off the (inability for) circumcision does not stop him from converting and it enough for him (just) to dip and so wrote going "a eunuch that comes to converted enters under the wings of the shechina as a woman (without circumcision)...
Into law we take the last opinion as it says in the Shulchan Aruch 268.1
גר שנכנס לקהל ישראל חייב מילה תחילה ואם מל כשהיה עובד כוכבים (או שנולד מהול) (טור בשם הרא"ש) צריך להטיף ממנו דם ברית ואין מברכין עליו ואם נכרת הגיד אין מילתו מעכבת מלהתגייר וסגי ליה בטבילה.
We do not circumcise our male children because this was commanded to Avraham. We do this for the same reason that we do all the mitzvoth. Because it was commanded to the Jewish people at the giving of the Torah. It is in remembrance of the covenant of Avraham (Shabbat 137b, Yoma 85b, Chagigah 3a).
There are two general elements related to the Brit. One is the removal of the foreskin and the other is the shedding of ones blood (Mishnah Torah, Hilchot Milah 3:4, Shulchan Aruch, Yorah Deah 268:1,2,5). The foreskin aspect is associated with the covenant of Avraham, that we are his descendants, members of his household and the inheritors of his blessing (Shulchan Aruch, Even HaEzer 129:20). This is also why all converts are called "ben (or bat) Avraham", the children of Avraham.
The second aspect pertaining to the shedding of ones blood in service to HaShem is the idea of personal "mesirat nefesh" the dedication of ones life to serving G-d like we say in the Shema, "with all your heart (both your good nature and your bad inclination), and with all your soul (your life), and with all your might (your wealth). This is also the intention that we say in the Haggadah at Passover when it states twice, "By your blood you shall live. By your blood you shall live." Once relates to the blood of the Korban Pesach and the second to the blood from the circumcision. This is also the explanation found in the Yalkut Shimoni on Yechezkel 354.
Like it states there quoting from Shemot 12:44, 48, non-Jews and the uncircumcised could not eat from the Korban Pesach at the time of the first redemption.
In this context, the distinction made by the Ittur and the earlier poskim is understood. That even when a non-Jew who has been circumcised by non-Jews comes to convert, he must have the drop of blood taken. Because this is the declaration of his dedication to serving G-d.
and the other is the shedding of ones blood source? | This is also why all converts are called "ben (or bat) Avraham", the children of Avraham. Source? | The second aspect pertaining to the shedding of ones blood in service to HaShem is the idea of personal "mesirat nefesh" Source?