Bekhorot 49A

בבא בהרשאה.

This is referring to a case where one of the fathers comes with authorization to act on behalf of the other father to state his claim for him, and therefore the priest cannot reject his claim. But if they gave the money to two different priests an authorization is of no effect, as each priest can claim the other took the redemption money of the son who died.

והאמרי נהרדעי: לא כתבינן אדרכתא אמטלטלי! הני מילי היכא דכפריה, אבל היכא דלא כפריה ⁠— כתבינן.

The Talmud asks: But didn’t the rabbis of Neharde’a say: We do not write an authorization document [adrakhta] concerning movable property? Therefore, in the case of redemption, where money, which has the status of movable property, is demanded from the priest, an authorization document may not be used. The Talmud answers: This statement, that one does not write authorization for movable property, applies only when the respondent, in this case the priest, already denied the claim against him. But in a case where the respondent did not yet deny the claim against him we write authorization even for movable property. In the case of redemption, although the priest claims the one issuing the claim against him is not the father of the son who died, he does not deny that he received the money.

זכר ונקבה ⁠— אין כאן לכהן כלום. תנא רב הונא: שני זכרים ונקבה ⁠— אין כאן לכהן כלום.

§ The Mishnah teaches: With regard to two women who had not previously given birth who were married to two men, and gave birth to a male and a female who then became intermingled, the fathers are exempt from the mitzva of redemption but the son is obligated to redeem himself, as he certainly has firstborn status. If the offspring were two females and a male, or two males and two females, all of whom became intermingled, the priest has nothing here. Concerning this case Rav Huna teaches: If they gave birth to two males and a female the priest has nothing here, despite the fact that one of them is definitely a firstborn, as each father can claim that his firstborn is the female. In addition, the sons are exempt as well, since each can claim that the female was his sister and born first.