The Patriarch (Batiryark) is the Sayedna (Bishop) who presides over a Synod of Sayedna. The Patriarch is the first among the Sayedna when they gather together to deliberate on matters common to their church.

First

According to tradition, the Patriarch (Batiryark) is the successor of The Holy, Glorious and Illustrious Prince of the Apostles Peter. Tradition maintains that the See of Antioch was founded by The Holy, Glorious and Illustrious Prince of the Apostles Peter in 45 AD.
The Holy, Glorious and Illustrious Prince of the Apostles Peter was appointed by Holy God the Son within the Holy Trinity / Our Lord, God and Savior, Jesus Christ to be His representative on earth. Then, the Patriarch is the representative of Holy God the Son within the Holy Trinity / Our Lord, God and Savior, Jesus Christ on earth.

Title

The Patriarchal Head of the Greek Melkite Catholic Church has the title "Patriarch (Batiryark) of the cities of Antioch, Alexandria and Jerusalem, of Cilicia, Syria, Iberia, Arabia Mesopotamia, Pentapolis, Ethiopia, of all of Egypt and the entire East, Father of Fathers, Pastor of Pastors, Bishop of Bishops, the Thirteenth of The Holy Apostles". His official title is Patriarch (Batiryark) of the city of Antioch, of Cilicia, Syria, Iberia, Arabia Mesopotamia, Pentapolis, Ethiopia, of all of Egypt and the entire East, Father of Fathers, Pastor of Pastors, Bishop of Bishops, the Thirteenth of The Holy Apostles.
Historically "Of Alexandria and Jerusalem" have been added as a personal title.
Patriarch Maximos III Masloum was elected in 1833. In 1838 he obtained from Rome the additional titles of Patriarch of Jerusalem and Patriarch of Alexandria as a result of the movement of the Melkite people throughout the Middle East.

Patriarchs (Batiryark) are usually addressed and referred to as "Patriarch first name". The formal written title is "His Beatitude, Patriarchal first name, Patriarch of the cities of Antioch, Alexandria and Jerusalem, of Cilicia, Syria, Iberia, Arabia Mesopotamia, Pentapolis, Ethiopia, of all of Egypt and the entire East, Father of Fathers, Pastor of Pastors, Bishop of Bishops, the Thirteenth of The Holy Apostles.
Patriarchs are not called "Patriarch last name".

Current Patriarch

The current Patriarch is His Beatitude, Gregorios III, Patriarch (Batiryark) of the cities of Antioch, Alexandria and Jerusalem, of Cilicia, Syria, Iberia, Arabia Mesopotamia, Pentapolis, Ethiopia, of all of Egypt and the entire East, Father of Fathers, Pastor of Pastors, Bishop of Bishops, the Thirteenth of The Holy Apostles.

Pope

Melkites recognize the Patriarch of the West as the successor of The Holy, Glorious and Illustrious Prince of the Apostles Peter. The title given to the successor is "Pope".
Melkites recognize the Patriarch of the West as "first among equals". "Equals" are the other Patriarchs, one of which is The Patriarch / Batiryark of Antioch.
The current Patriarch of the West and Pope is His Holiness Ioannes Paulus II (John Paul II).

Historically, the patriarchs have had an order of precedence. The Patriarch of the West (the Pope) is the First. After the Patriarch of Constantinople (the Ecumenical Patriarch) was established, it became second. This event happened after the capitol of the Roman empire was moved to Constantinople. In 381 A.D., Constantinople was elevated to a Patriarchal See and given the ranking of "second only to the See of Peter" (the See of Rome).