Before us is Mishnah 2 in the eleventh chapter of Maseches Yevamos. The Mishnah rules: "Hagiyores shenisgayru baneha imah - lo choltzin v'lo meyabmin" - a woman who converted and whose sons converted along with her, her sons are not bound to one another either for chalitzah or for yibum.
The reason: there is no brotherhood through the father:
The reason is that there is no brotherhood between them: the bond of brotherhood that is based on the father does not apply to someone who was not Jewish.
Even where the conception was not in sanctity and the birth was in sanctity:
The Mishnah teaches that this ruling does not apply only to a case in which both the conception and the birth of the two brothers took place before they converted, but even in the following case:
The first brother - his conception was not in sanctity and his birth was in sanctity: the conception took place before they were Jewish, while the birth occurred after they were already Jewish.
The second brother - both his conception and his birth were in sanctity: both the conception and the birth occurred after they were Jewish.
Even though the only element lacking here is the conception of the first brother, which took place at a time when his father was not yet Jewish, that alone is enough for there to be no brotherhood between them through the father.
A maidservant whose sons were freed along with her:
The same law applies to a maidservant whose sons were freed along with her. A maidservant is like a partial convert, and from the moment she was freed together with her sons they all became full Jews, so that they are parallel to converts. They too do not perform chalitzah or yibum for one another, since part of their coming into being took place before they were Jewish, and therefore there is no brotherhood between them through the father.
In summary: in this Mishnah we learned that a convert whose sons converted along with her - her sons do not perform chalitzah and do not perform yibum, because there is no brotherhood through the father for one who was not Jewish. This law applies even when one brother's conception was not in sanctity and his birth was in sanctity, while the second brother's conception and birth were both in sanctity, since it is enough that the conception took place before the conversion. The same law applies to a maidservant whose sons were freed along with her, who are parallel to converts.