It’s one I was unaware of until meeting a young woman today of that path. Googling reveals that Medyen is the name of a place in, I think, the Qur’an, (“Moses, son of Imran (a.s.), was another immigrant in the cause of God for he left his country, Egypt, and headed for Medyen.”) and also the name of a Sufi (Ebu Medyen).
The Quranic passage alludes to a Torah passage, in Exodus in English translations. When Moses fled Egypt after killing the overseer, he went to Midian, for which Medyen is a fairly good Arabic rendering, as is Madyan. See the Wikipedia article for location and Scriptural context. Moses married the daughter of a man variously termed Reuel and Jethro who was a Midianite, and was “priest of Midian.” Midianites appear to have been the original Yahwists.
It’s actually transliterated Madyan from Arabic مدين. You may have come across a Turkish source, going by the spelling (some of the a’s get changed into e’s in Turkish).
Madyan is nothing more or less than the Arabic form of Midian, a place in northwestern Arabia where Moses fled from Egypt. The name turns up in the Qur’ān in connection with the story of Moses.
Abu Madyan was a prominent 12th-century Spanish Sufi of the Shadhili order. A very famous name if you’re Shadhili, not so much to anyone else. A book about him that came out a few years ago is The Way of Abu Madyan by Vincent Cornell.
As to what this woman you met could have meant by “of that path,” I have no idea, unless she’s Shadhili. “Path” is a word that often refers to a given Sufi order. There’s no religion named Medyen or anything like that. Unless they’ve come up with a new religion since the last time I looked. But the only religion connected with the name is Islam.
Trivia: The former leader of Algeria, Boumédienne, is actually named after Abu Madyan, filtered through a French spelling of the Algerian dialectal pronunciation.
She told me the name orally, so the spelling is my best guess, based on some internet searches for similar sounding words. I may be leading us off with a red herring here.
Ask her if she’s Shādhilī.
Trivia: Another Algerian leader, named Chadli, is named with the French spelling of the Algerian dialectal pronunciation of Shādhilī. In Tunisia it’s spelled Chedli, rhyming I think with medley.