I think you are referring to the Coptic Orthodox Church. This Church split from the Orthodox and Catholic churches in the Chalcedon Council of the fifth century. Their catechism and ritual are very similar to Catholic and Orthodox theology: they believe in the divinity of Christ, the true presence of Christ in the Eucharist and the clerical hierarchy, etc. Their main dispute with other churches is in their understanding of the incarnation: whether Christ was of two natures and both fully divine and human. There are other Coptic Christians, however, Melkite Catholics and Greek Orthodox Christians.