Tyrafferty seems to be one of several alternate spellings for the townland of Teraverty which is in Tedavnet civil parish Co. Monaghan
Tydavnet is an alternate spelling for Tedavnet, a civil parish in Co. Monaghan.
So strictly speaking Tyrafferty/Teraverty townland is part of Tedavnet / Tydavnet civil parish
incidently one of the other ~150 townlands within the civil parish of Tedavnet is also named Tedavnet
see the placename database for details
Teraverty Tedavnet (civil parish) and
Tedavnet (townland)
see the section marked archival records for some of the alternate spellings