The Ethiopian Church I will mostly talk about in this post is the “Ethiopian Orthodox Tewahedo Church”, it is part of the Oriental Orthodox communion.

According to its own traditions, Christianity came to Ethiopia through the “Ethiopian Eunuch” of Acts 8. It is very difficult to substantiate this in any way though.

Church Historian Rufinus (Historia Ecclesiastica I.ix) records missionary work in Ethiopia during the 4th century. Although it appears there were already some Christians there, the shipwreck of Frumentius and Aedesius who later found royal favour under King Ezana of the Axumite kingdom, and a privileged position. Frumentius in particular may have been responsible for organising local Christians. And with authorisation from Athanasius of Alexandria, Frumentius was consecrated in Dec 330 as the first bishop of Ethiopia. You can read Theodoret’s account of this in Historia Ecclesiastica 1.21, though he talks about “India”, but India was a very vague reference at the time, and there was some belief that Africa and Asia were connected ‘further south’. There is also attestation to this in Athanasius’ Defence before Constantine 30, which contains a Letter of Constantius to the Ethiopians, which is aimed at bringing Frumentius to trial, since he had been appointed by Athanasius, and so associated with his pro-Nicene doctrines, while Constantius was very much anti-Athanasius. Conversion efforts overall appear to have been quite successful, and Ethiopia became a majority Christian country, the Bible and liturgy were translated into Ge’ez. From sometime in the late 5th century Syrian Christians introduced monastic practices into Ethiopia.

The church’s close association with Alexandrian Christianity and the Christological debates of the 5th century meant that the Cyrilic doctrine of Monophysites prevailed not only among Egyptian Copts, but Ethiopian Christians, leading the Ethiopian church to remain aligned with Alexandrian doctrine and practice. That is why the majority church in Ethiopia is part of the Oriental Orthodox Communion.

Insofar as Mediterranean Christianity was much more cohesive in Late Antiquity than later, I would certainly say that “Roman Christianity” ‘knew’ about Ethiopia, though it was always ‘far off’, being beyond imperial borders. However, if we are discussing the 1100-1400 period, I can’t say for certain, as this is after the Great Schism of 1054, and Roman Catholic interest was by then centered in Continental Europe. Furthermore, North Africa was lost first to the Vandals, and then Ethiopia was effectively cut off from Europe by the Islamic/Arabic conquests through North Africa in the 8th century. Ethiopia then became one ‘location’ for the development of fables about Prester John’s Lost Christian Kingdom.

Can you specify a time period?

/u/talondearg has given a great response. I also urge you to check out information on the legends of Prester John. Many modern scholars believe that this mythical leader arose from the somewhat scant knowledge of there being a Christian community in Ethiopia. I'm sure one of the other historians more familiar with the Crusades and Prester John could give some great resources and information. :)