Both me and the other poster in this thread have posted links on the overlap between Rusyn and Ukranian identities in Eastern Slovakia. The Magyar identity is centered around the Hungarian language and Roman Catholicism or Protestantism, while any history of the Rusyn people will emphasize how they are East Slavic-speaking Greek Catholics, so why you feel that the Magyars are relevant here is beyond me. Some of the Rusyn-speaking world was under Austrian administration in the Austro-Hungarian Empire, so they weren’t even under Hungarians politically.