There have never been "orthodox church" pope. Pope is considered to be one of five Patriarchs of Chalzedonian Christianity. The East-West Schism occured due to many differences but one of reasons was that Pope is a descendent of Saint Peter and wanted to remain a head of the church but other Patriarchs (especially of Constatninople) wanted to be autonomous.

Basically Western Schism happened because in 1378 people in Rome rioted and wanted the Pope to be Roman. So under this pressure and death thread cardinals decided to choose someone who was italian.

So when it all was over some of the cardinals refused legimacy of this pope and chose another one in Avignion (before 1377 this was a place where papacy have been ruling from for a century).

So we had 2 popes now. 1 in France and 1 in Rome.

Later there was a pressure from the Emperor of the HRE to end this conflict. It resulted in creating even third pope who was supported by the Emperor.

I highly reccomend "Anneau du pêcheur" by Jean Raspail, 1995. It's a fiction but based on real history.

Could you possibly be referring to the Catholic Schism? This is the most famous instance of two rival popes claiming leadership of the Roman Catholic Church, when one pope ruled in Rome and another in Avignon in France. There are also other, more obsure cases of multiple popes, which you can find a list of here.

The occurrence of multiple popes ruling separate parts of western Catholic Christendom at the same time isn't all that uncommon in medieval Europe. Popes and antipopes would both claim legitimacy, but were appointed and could oppose one another for numerous reasons.

One example is antipope Clement III, who was appointed by Emperor Henry IV after the regular pope, Gregory VII, excommunicated the emperor in 1076 for demanding secular control over ecclesiastical appointments. This was an outcome of the much wider ongoing conflict between the Church and the Holy Roman Empire concerning investiture (the principles of emperors nominating popes, and popes crowning emperors). Considered an imperial puppet, Clement greatly opposed several anti-imperial popes (some of whom were forced into exile), but eventually lost control as Henry's power waned.

The Great Papal Schism of the late fourteenth and early fifteenth century is another extended period in which popes opposed one another, one ruling from Rome and the other from Avignon. The papacy had already been based in Avignon for some time, but returned to Rome in 1377, where a new pope, Urban VI, was appointed in the following year. Several cardinals regretted their decision to pick Urban, as he turned out to be a reformist, and appointed Clement VII instead, who set up shop in Avignon once again.

Sources: Tierney's Crisis of Church and State (Primary sources) Blumenthal's Investiture Controversy

An introduction to the Western Schism can be found in Lynch and Adamo's Medieval Church: A Brief History