Did the Apostolic Church Fathers write about the capacity in which women were to serve in the early church, or expand the capacity in which they served the church? In other words, what were they responsible for as far as the Apostolic Church Fathers were concerned? As the church grew did their responsibilities grow as well?
The woman Grapte referred to in I.2.IV of the Shepherd of Hermas is understood to have been a deaconess. The duties of deaconesses, however, are not understood to be equivalent to those of deacons, but involved, rather, ministering to widows and orphans, and perhaps helping to prepare and baptize women. The above passage is an example:
You will write therefore two books, and you will send the one to Clemens and the other to Grapte. And Clemens will send his to foreign countries, for permission has been granted to him to do so. And Grapte will admonish the widows and the orphans.
The Apostolic Constitutions, which may have been published long after the Apostolic Fathers, but is thought by many to represent the teachings of both them and the Apostles, provides additional details about the roles of deaconesses:
For let the bishop preside over you as one honoured with the authority of God, which he is to exercise over the clergy, and by which he is to govern all the people. But let the deacon minister to him, as Christ does to His Father; and let him serve him unblameably in all things, as Christ does nothing of Himself, but does always those things that please His Father. Let also the deaconess be honoured by you in the place of the Holy Ghost, and not do or say anything without the deacon
In the next place, let the presbyters one by one, not all together, exhort the people, and the bishop in the last place, as being the commander. Let the porters stand at the entries of the men, and observe them. Let the deaconesses also stand at those of the women, like shipmen. For the same description and pattern was both in the tabernacle of the testimony and in the temple of God
Ordain also a deaconess who is faithful and holy, for the ministrations towards women. For sometimes he cannot send a deacon, who is a man, to the women, on account of unbelievers. Thou shalt therefore send a woman, a deaconess, on account of the imaginations of the bad. For we stand in need of a woman, a deaconess, for many necessities; and first in the baptism of women, the deacon shall anoint only their forehead with the holy oil, and after him the deaconess shall anoint them
There also appears to be a prohibition against women baptizing:
Now, as to women’s baptizing, we let you know that there is no small peril to those that undertake it. Therefore we do not advise you to it; for it is dangerous, or rather wicked and impious. For if the “man be the head of the woman,” and he be originally ordained for the priesthood, it is not just to abrogate the order of the creation, and leave the principal to come to the extreme part of the body. For the woman is the body of the man, taken from his side, and subject to him, from whom she was separated for the procreation of children. For says He, “He shall rule over thee"