The Coptic Orthodox Church split from Rome in the fifth century. There’s 57 million Coptic Orthodox Christians worldwide. They continue to represent 95% of Christianity in Egypt.
The Coptic Catholic Church represents around 200,000 Coptic Christians (mostly in Egypt) that have returned to full communion with Rome. This has happened in just the last couple of centuries.
There were a number of false starts and bumps in the road along the way for the Coptic Catholic Church. (Remember that this all happened no earlier than the 18th century, even though many of these people took names that are more readily associated with a much earlier time).
In 1741, a Coptic bishop from Jerusalem named Ambad Athanasius became Catholic and brought about 2,000 people with him. He later reverted to Orthodoxy, but his Catholic office of Vicar Apostolic stayed put. (Not to be confused with a more famous Athanasius, who lived in Egypt but pre-dated the Coptic schism).
In the 1820’s, a Coptic Catholic Patriarchate was established in Egypt. At the beginning of this decade, it was on paper only, but by the end, Coptic Catholic churches were actually being built. This process faced an uphill battle (as most things Christian do in Egypt) because of the Ottoman authorities.
At the end of the 19th century (right around the turn of the 20th), the Coptic Catholic Patriarchate in Egypt had to be re-established. Bishop Cyril Makarios became Cyril II, he resigned in 1908, and the position remained vacant until 1947.
The Coptic Catholic church now has a bit more stability in its leadership and succession, but this has only happened in the last couple of generations. Copts, whether Catholic or Orthodox, join the Ethiopian Christians in practicing the Alexandrian rite. Coptic Catholics do have some Roman influence in what they do, though, while the Coptic Orthodox have little to none. The Alexandrian rite is divided into the Coptic rite (Egypt) and the Ge’ez rite (Ethiopia).
This thread
forums.catholic-questions.org/showthread.php?t=364416 has quite a few links on the Alexandrian rite. Those contributions were made in August of '09, but as I’m posting this, the senior member who contributed to that thread is online. So that’s one currently active member that you can track down. Click on that name (or the name of anyone else who seems helpful), look up recent posts, and see if they’ve been active lately. If you see plenty of recent activity in the Eastern Catholicism sub-forum, it shouldn’t be too hard for you to strike up a bit of correspondence with these kinds of people. Go to that sub-forum, start another thread, maybe change the wording a little if that will help, and start making mental notes of who can help you the most right now. They’ll probably contribute something to the new thread on their own, but it helps if you already know who’s currently active along with being knowledgeable in this area. You’ll be able to look for them and pursue more information from these specific people because you’ll know they have it.