Please note the Maronite Rite and Malabar Rite in particular, which is in Lebanon and India. These started in the East around the 4th Century and never went into schism with Peter not even in 1054! These never went into heresy either.
The Rites of the Catholic Church as described by Catholic News Agency:
It may surprise most people to know that there are many different rites within the Catholic Church. Before discussing these rites it is important to note that different sources disagree on exactly what constitutes a rite and exactly how many there are.
A rite represents an ecclesiastical tradition about how the sacraments are to be celebrated. As the early Church grew and spread, it celebrated the sacraments as would be best understood and received in the context of individual cultures, without ever changing their essential form and matter. The early Church sought to evangelize in the major cultural centers of the first centuries A.D. These centers were Rome, Antioch (Syria), and Alexandria (Egypt). All the rites in use today evolved from the liturgical practices and ecclesiastical organization used by the churches in these cities.
The Church of Christ represented in these ecclesiastical traditions is known as a ritual church. The church in a certain territory is known as a particular church.
The Catholic Encyclopedia describes the situation this way: "Within the Catholic Church ... Canonical rites, which are of equal dignity, enjoy the same rights, and are under the same obligations. Although the particular churches possess their own hierarchy, differ in liturgical and ecclesiastical discipline, and possess their own spiritual heritage, they are all entrusted to the pastoral government of the Roman pontiff, the divinely appointed successor of St. Peter in the Primacy.
The Catechism lists seven rites. These rites so listed: Latin, Byzantine, Alexandrian, Syriac, Armenian, Maronite, and Chaldean, 2 are actually families of liturgical expression. These rites are the descendants of the liturgical practices that originated in centers of Rome, Antioch, and Alexandria. Each will be discussed in turn.
LATIN. The Pope has several titles. He is the Bishop of Rome, Vicar of the universal Church, Primate of Italy; among others. As the Bishop of Rome he is the head of the Latin or Roman rite. This is by far the largest rite in the Church. It was founded by St. Peter in Rome around 42 A.D. The current Eucharistic liturgy was handed down more or less intact from at least the 4th century. This was the liturgy used in Rome. There were other liturgies used in the West up to the Council of Trent (1526-1570). After the Council of Trent only the Roman liturgy could be used. The only exceptions were liturgical practices that were more than 200 years old.
The Pope is also vicar of these other liturgical rites that date from before the Council of Trent. These rites include the Mozarabic rite from Spain, the Ambrosian rite from Milan, Italy, named after St. Ambrose (340-397), the Bragan rite from Portugal, and the order liturgies of the Dominican, Carmelite, and Carthusian orders.
As Vicar of the universal Church, the Pope is shepherd of the rites of the West and the East. The eastern rites which have a separate code of canon law, are completely equal in dignity with the rites of the West. All of these eastern ritual churches come under the jurisdiction of the Pope through the Congregation for the Oriental Churches, one of the offices of the Roman Curia. The rites are administered by either a Patriarch, a Major Archbishop, a Metropolitan, or have some other arrangement. Patriarchs are elected by a synod of bishops of their rite, and then request ecclesiastical communion from the Pope. Major Archbishops are also elected by a synod of bishops of their rite, but then are approved by the Pope before they take office. Metropolitans are picked by the Pope from a list given by a synod of bishops.
BYZANTINE. The largest of these eastern rites is the Byzantine. The Byzantine liturgy is based on liturgy developed by St. James for the Antiochaian church, but modified by St. Basil (329-379) and St. John Chrysostom (344-407). This liturgy is similar if not identical to the liturgy used by the Orthodox churches. After the schism between the churches in Rome and Constantinople in 1054, many particular churches remained separated from Rome. Over the years some of these churches came back into union. These churches after they returned to the fold have generally been treated as separate rites based on their particular location, even though they have similar if not identical liturgy. The churches using the Byzantine liturgy include the Albanian, Belarussian, Bulgarian, Croatian, Greek, Hungarian, Italo-Albanian, Melkite, Romanian, Russian, Ruthenian, Slovak, and Ukrainian.
ALEXANDRIAN. The liturgy used by the church in Alexandria in Egypt is attributed to St. Mark the evangelist. This church became known as the Coptic church because Copt is the Arabic and Greek word for Egyptian. Before the Moslem invasion in 641 the Copts fell into heresy due to their rejection of the Council of Chalcedon (451). Through missionary work, some of these were brought back into union in recent years. Today there exists in Egypt the Coptic rite which is Orthodox and the Coptic rite that is loyal to the Bishop of Rome.
The Ge'ez rite based in Ethiopia is closely associated with the Coptic rite. Missionaries from Alexandria spread the faith in Ethiopia in the 4th century. The native language (Ge'ez) was used instead of Greek in the liturgy. The church in Ethiopia also fell into heresy after the Council of Chalcedon but was brought back through missionary efforts in the past few centuries. This is a very recently defined rite since the Metropolitan See was only established in 1961.
SYRIAC. The liturgy of the Syriac rite is attributed to St. James the Apostle. This liturgy was used by the church in Antioch in present day Syria. Many bishops in this area also broke away after the Council of Chalcedon. They stopped using Greek and used the Syriac language in their liturgy. The Syriac language is similar to Aramaic, the language Jesus spoke. Through the work of Jesuit and Capuchin missionaries many members of this rite returned to union with Rome, including the Patriarch of this rite in 1781.
The Malankarese rite developed in India. They trace their Christian lineage to St. Thomas the Apostle who traveled to South India and founded a church. This rite was in union with the Assyrian (Chaldean) church which had fallen into the Nestorian heresy after the Council of Ephesus in 431. This church was "discovered" by Portuguese missionaries in the 16th century. After attempts to "latinize" the rite, many broke away to form their own rite under the control of the Syrian Patriarch. In the 1920's and 30's four bishops of this rite were reunited with Rome, and many members of their rite followed. This rite is located in Kerala State, India.
ARMENIAN. Armenia was the first country to adopt Christianity as the state religion in the 4th century. They used the Antiochine liturgy of St. James said in the Armenian language. At that time Armenia was located in eastern Turkey. After it was destroyed in the 11th century it moved to Cilicia (southern Turkey). That is why to this day the Patriarch of this rite is known as the Patriarch of Cilicia of the Armenians. The Armenians also fell into heresy after the Council of Chalcedon. The Council of Florence in 1439 declared reunion with the Armenians, and Pope Benedict XIV confirmed the first Patriarch in 1742. The Turks massacred roughly two million Armenians at the end of World War I. Most members of this rite live in Lebanon.
MARONITE. The Maronite rite traces its origins to the work of St. Maron in the 4th century who founded a monastery east of Antioch. Later monks moved to the mountains in what is today Lebanon. This rite never fell into heresy and was only separated from Rome by the political reality of Moslem or Ottoman occupation. The Maronites use a hybrid liturgy based on the Antiochian St. James. Maronites make up 17% of the population of Lebanon and by the law of that country the president of Lebanon is always a Maronite.
CHALDEAN. The people in modern day Iran and Iraq were once known as the Assyrians. The church established itself there very early but the people in this area fell into the heresy of Nestorianism in the 5th century. After missionary efforts many returned to union with Rome, and in 1553 Pope Julius III proclaimed the first Patriarch of the Chaldeans. Chaldean is the biblical term used for those from Babylon. Today the Patriarch of this rite located in Bagdad, Iraq where most of the members of this rite live.
SYRO-MALABAR: The Malabar rite is based in India. Its members are descendants of the Thomas Christians and could be called a brother rite to the Malankarese. The Malabar rite never broke with Rome despite the conflict with the Portuguese in the 16th century. They are generally grouped with the Chaldean family of rites because the Assyrian (later called Chaldean) church provided their bishops until the Portuguese took over that task. Also their liturgy was originally in the Syriac language which the Chaldean church used. Although an ancient rite, it had no single administrator until Pope John Paul II appointed a Major Archbishop in 1992.
All the rites of the Catholic Church are of equal dignity and equally valid. Attendance at a different rite fulfills the Sunday obligation. The Catholic Church is truly universal since it unites so many diverse rites, whose members share a common faith.