Yevamos, Chapter 11, Mishnah 7. This mishnah too deals with a widow who did not wait three months after her husband's death, remarried, and gave birth to a child seven months after her second marriage, so that it is unknown which of the two men is the father. Here, however, the mishnah discusses a case in which one of the husbands was a Yisrael and the other a kohen, and it addresses the halachic consequences of this doubt - not regarding chalitzah and yibum, but regarding the laws of kehunah and other matters.
"Hayah echad Yisrael ve'echad kohen":
One of the husbands was a Yisrael and the other a kohen, and we do not know whether the son is a Yisrael or a kohen. From here the mishnah lists a series of laws that follow from this doubt:
"Nosei ishah re'uyah lechohen" - he may marry only a woman who is permitted to a kohen. He does not marry a divorcee or a convert.
"Ve'eino mitammei lemeisim" - he is forbidden to become tamei to a corpse, out of concern that he is a kohen.
"Ve'im nitma, eino sofeg es ha'arba'im" - beis din does not administer lashes to him for this transgression, since we do not administer lashes where there is doubt.
"Ve'eino ochel biTerumah" - perhaps he is not a kohen.
"Ve'im achal, eino meshalem keren vechomesh" - we collect from him neither the principal nor the added fifth, since perhaps he is a kohen and the Terumah was rightfully his.
"Ve'eino cholek al hagoren" - he is not given a portion of the Terumah distributed at the threshing floor, since he cannot prove his entitlement.
"Umocher es haTerumah, vehadamim shelo" - Terumah that has come into his possession he may sell, and the proceeds remain his, for one cannot extract money from the one who holds it.
"Ve'eino cholek bekodshei haMikdash" - not even in sacred items that are not eaten, such as the hides of the offerings, since in order to acquire something not already in his possession he would have to prove that he is a kohen.
"Ve'ein nosnin lo es hakodashim" - offerings are not handed over to him to sacrifice, and likewise he is not given the priestly gifts that involve no service, such as items dedicated to the kohanim by cherem.
"Ve'ein motzi'in es shelo miyado" - offerings that are in his possession are not taken from him, and he is not compelled to hand them over to the kohanim of the watch serving that week. He may assign the service to any kohen he wishes, for this service has monetary value, and it is in his power to grant it to whomever he chooses.
"Ufatur min hazero'a vehalechayayim vehakeivah" - one who slaughters a non-sacred animal must give the kohen the foreleg, the cheeks and the maw. Here he is exempt, since this is a monetary gift and not something reserved for consumption by kohanim alone, for a Yisrael eats it as well.
"Uvechoro yehei ro'eh ad sheyista'ev" - a firstborn animal born to him is not handed over to a kohen; rather it grazes until it develops a blemish, and once it is blemished even he may eat it, for one need not be a kohen in order to eat a blemished firstborn.
"Nosnin alav chumrei kohanim vechumrei Yisraelim" - as we have already noted in an earlier mishnah, this phrase refers to the laws of the meal offering. In the meal offering of a Yisrael, a handful is scooped out and burned on the altar, and the remainder is eaten by the kohanim; whereas the meal offering of a kohen is burned in its entirety. Therefore both stringencies are applied to him together: a handful is scooped out and burned - like the stringency of a Yisrael, and the remainder is not eaten by the kohanim but burned in the place of the ashes, where disqualified offerings are burned - like the stringency of the kohanim.
"Hayu shneihem kohanim":
If both husbands were kohanim, then the son is certainly a kohen, and therefore: "Hu onen aleihem" - the son observes aninus for both of them. Aninus is a person's status before the burial of his relative, during which he is exempt from mitzvos, and with regard to kehunah - he does not perform the service in the Mikdash.
How is it possible for him to be an onen for both of them?
Seemingly, the sequence of events is that the first husband died, and only afterward did she marry the second and give birth to the son - so what room is there for aninus over the first? And we cannot say that she was divorced from the first, since a divorcee is forbidden to the second husband, who is a kohen. The answer is that the aninus over the first father takes place at the time of the gathering of the bones, when he is reburied; on that day the law of aninus returns. It emerges that he observes aninus for the first at the time his bones are gathered, and for the second at the time of his death.
A more complex issue arises from the continuation: "Vehem onenin alav" - both fathers mourn for the son if he should die. And further: "Hu eino mitammei lahem vehem einam mitamm'in lo" - the son does not become tamei for either of them, and they too do not become tamei for him.
How is it possible for both fathers to be alive at the time of the son's death?
This requires that both of them be alive when he passes away, and the previous answer - the gathering of bones - does not help here, since in order to observe aninus over the son the first father must be alive. And if we were to say that she was divorced from the first and married the second unlawfully, then the son is a chalal and is not a kohen at all, and consequently he would have been permitted to become tamei: if he is the son of the second - that is literally his father and he becomes tamei for him, and if he is the son of the first - he is a chalal and not a kohen. This, then, is not a possibility.
Rather, the case is one in which the first husband betrothed her conditionally, and the condition was not fulfilled, so that retroactively the betrothal was no betrothal at all. Even though a child was born to them, halachically they were never married, and therefore she was permitted to the second husband, who is a kohen.
The mishnah continues: "Hu eino yorshan, aval hem yorshin oso" - the son does not inherit from the fathers, since the other heirs push him off with the claim that he cannot prove that he is the son of this particular father. But if the son dies, both fathers inherit from him and divide the estate equally.
We further learned: "Ufatur al makaso ve'al kilelaso" - one who strikes his father and causes a wound, and likewise one who curses his father, is liable to death. Here, however, if he struck one of the fathers or cursed him - he is exempt, since it cannot be proven that he is the son of that father.
"Ve'oleh bemishmaro shel zeh veshel zeh, ve'eino cholek" - since both are kohanim, he must go up and serve during the week of each father's watch, as a stringency. But he is not given a portion of the offerings, since he cannot prove that he belongs to the watch of that week. "Ve'im hayu shneihem bemishmar echad, notel chelek echad" - for either way he belongs to the watch of that week. It is worth noting that since each watch is subdivided into fathers' houses, family groups that serve on different days, the two must also belong to the same fathers' house and serve on the same day in order for him to receive that one portion.
In summary: in this mishnah we learned the law of a child whose father may be either a Yisrael or a kohen. In the case where one husband is a Yisrael and one a kohen, we impose upon him the stringencies of kehunah - the prohibition against marrying women unfit for a kohen, the prohibition against becoming tamei, and the prohibition against eating Terumah - but we do not punish him and do not extract money from him where there is doubt, nor do we give him a portion of Terumah or of the sacred items; and with regard to his meal offering we apply the stringencies of kohanim and the stringencies of Yisraelim together. And in the case where both husbands are kohanim, we learned the laws of mutual aninus - resolved through the gathering of bones and through a conditional betrothal whose condition was not fulfilled - the laws of inheritance, the exemption for striking and cursing his father, and the law of his going up to serve with the watches and the division of the sacred portions.