The Patriarch of Constantinople is held to be the head of the Eastern Orthodox Churches, but in fact has no seniority over any other bishop. The Eastern Churches split from the Catholic western churches partly because the western communion insisted on a special authority for the Roman pope. So the Patriarch of Constantinople would be a very clear case of a primus inter pares.
But there are many other possible examples, as you will find at the link offered.
What was the patriachate regarded as the "first among equals"
The Patriarch of Rome was regarded as "the first among equals".
Andrew Fraser - First Among Equals - was created in 1984.
NZSAS First Among Equals - 2007 is rated/received certificates of: New Zealand:PG
It means the "first among equals"
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Primo fra pari.
A patriarch is the just a Bishop who was selected by his brothers in Christ to be the leader of the Church . The first among the equals.
Ecumenical Patriarch and he is the "first among equals" and by no means infallible.
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There are many Orthodox patriarchs, but if you are referring to the Ecumenical Patriarch (who is first among equals) then his name is His All Holiness Bartholomew I of Constantinople.
20 and 13, among others.