Is the Patriarch of Alexandria an Eastern Orthodox or an Oriental Orthodox? I see Eastern Orthodox keyboard warriors commonly posting memes, bite size apologetics and propaganda against Catholicism which make some variation on the claim "4 out of 5 Patriarchs choose Eastern Orthodoxy. You should too".

I was wondering how much veracity is behind this claim. I was under the impression that the Patriarch of Alexandria wasn't even in communion with the Eastern Orthodox church at all. I thought he was a Copt and a member of the Oriental Orthodox communion instead? Likewise for Jerusalem and Antioch. I thought that the only Patriarch of the original Pentarchy that is an actual Eastern Orthodox is the Patriarch of Constantinople?

My understanding is that 1 out of 5 Patriarchs chooses Catholicism, 1 out of 5 Patriarchs chooses Eastern Orthodoxy, and 3 out of 5 Patriarchs choose Oriental Orthodoxy. Please help me understand this situation further?
St Mark the Evangelist is recognised as the first Patriarch of Alexandria. The twenty-fifth was Dioscorus. In 449 he presided over the Second Council of Ephesus. Two years later another Council, regarded by Rome and Constantinople as the Fourth Ecumenical Council, was held at Chalcedon. The Council of Chalcedon repudiated the Second Council of Ephesus, known as the Robber Synod, and deposed Dioscorus, sending him into exile, where he died in 454.     

Proterius was chosen to replace Dioscorus but not widely accepted by many Alexandrians who still regarded Dioscorus as their patriarch. When Dioscorus died Timothy Aelurus (the cat) was chosen as non-Chalcedonian patriarch of Alexandria and is said to have arranged the murder of Proterius on Easter Day 457. The final split came in 536 since when there have been two separate patriarchs of Alexandria, the Coptic one (oriental Orthodox) supported by most Egyptian Christians, and the Eastern Orthodox one supported by Constantinople. (This is somewhat similar to Armagh in the UK where both C of I and RC primates of Armagh clain continuity from St Patrick.) 

From the thirteenth century there was also a titular Latin Patriarch, and in recent centuries a "Coptic Catholic" patriarch leading an Oriental Rite Catholic Church in communion with Rome. The Latin patriarchate was abolished after Vatican II. 

The only two in a continuous line from St Mark are the Coptic patriarch  and the Eastern Orthodox patriarch. The Coptic Patriarch, Pope Tawadros II, is recognised by over 90% of Egyptian Christians. His name was picked at random from a chalice containing three names by a blindfolded boy in 2012.    

There is, then, an Eastern Orthodox Patriarch of Alexandria of ancient lineage,  but the great  majority of Egyptian Christians, now and across the centuries, have accepted  the Oriental Orthodox Coptic Patriarch, also of ancient lineage, as head of the African Church.