Who wrote the Sub Tuum Praesidium? The Sub Tuum Praesidium is the oldest known hymn to the Virgin Mary, dating back to somewhere between 250-280. Has any Saint or Church Father ever been ascribed as being the author of this prayer?
As far as research on this goes, I couldn't find a single source which ascribes this prayer to any particular church father, and I doubt any church father is the author.

I found an interesting article on this prayer and its origins. You can find it here.

It says,


  "Besides the Greek text, ancient versions can be found in Coptic, Syriac, Armenian &amp; Latin.
  In Latin, the version used by the Roman rite has surely been done directly on the Coptic version of the text
  (like in Coptic, it uses the term 
  præsidium
   instead of 
  misericordia
  ) without going through the Greek. The
  Ambrosian form of the text closer depends on the Byzantine tradition"


It would appear from this that the Greek version is the original, but there are others versions used close to that time.

As to its use in the liturgy at the time of its writing:


  _"The antiphon was used at vespers during Christmas time in the Coptic liturgy. It is also known in Byzantine,
  Roman and Ambrosian rites. In each of these rites, though venerable &amp; ancient, the 
  Sub tuum præsidium
   has
  a discreet place, very marginal one might say
  
  ...
  
  Historically, the oldest evidence of the use of 
  Sub tuum
   in the Roman rite is found in the antiphonal of
  Compiègne (from the IX-Xth century), which provides it among the Benedictus antiphons for the Feast of the
  Assumption (Migne, PL 78, 799)..."_


As to the dating of the papyri itself and thus most likely the prayer itself, it says


  "[it has been dated] from the fourth
  century, thinking it was impossible to find an invocation to the 
  Theotokos
   before this century (we’ll see below,
  however, that the expression 
  Theotokos
   was in use in Alexandria before 250). But his colleague E. Lobel, with
  whom he collaborated in editing the Oxyrhynchus papyri, based on pure paleographic analysis, said the text
  can not possibly be later than the third century, probably dating between 250 &amp; 280".


Of course you gave the dating in your question but there really are no resources on who actually is the author, especially none showing that a church father was the author.