The writings of the Fathers of the Church are mostly in Greek and Latin. A Catholic priest named Migne once published 217 volumes of the writings of the Latin Fathers and 161 volumes of the Greek Fathers. The Latin set is called the Patrologia Latina and the Greek set is called the Patrologia Graecae.
When historians study the writings of the Fathers, that’s generally the set they go to, and they are available to the public. In fact, Google Books has scanned them and released their scans into the public domain, so you can actually read them online for free. But, of course, you would need to know Latin and/or Greek, because they haven’t all been translated into English.
That is the most complete set of the Fathers of the Church. But, believe it or not, even that is incomplete. Some writings of the Fathers are still being discovered in the ancient libraries of monasteries and in old parchments that have been erased and written over with other material. (Scholars can erase the new material while preserving the old, which makes it easier for them to find ancient “lost” texts, which are still being discovered in our time.)
In English, there are two major sets of the Church Fathers that scholars study if they don’t know Latin or Greek. One is a set of translations made in the early 1900s by Phillip Schaff, an Anglican historian. His set is a 38 volume collection that is organized into the Ante-Nicene Fathers, meaning Fathers who wrote before the Council of Nicaea in 325 A.D., and the Post-Nicene Fathers, which are the ones who wrote after that Council.
Besides his set, which is in the public domain and is available at newadvent.org/fathers, there is another set of English translations published by the Catholic University of America. They are still translating and publishing two new volumes each year, and they have currently published over 120 volumes of the Church Fathers in English, which makes their collection the most complete set of the Fathers available in English. (Read more here: cuapress.cua.edu/books/series.cfm) It is obviously very hard to purchase all the available volumes, but if you get the Verbum software from Logos Bible Software, you can subscribe to searchable ebook versions of (I think) every volume they’ve published, for a monthly fee.
Anyway I hope that helps. God bless!