How were women to serve the church according to the Apostolic Fathers? 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"