Where is this place in Leitrim?

[aghadowey]

Registration of births started in 1864- the civil registration index is online (free) and will give you the details needed to order a birth certificate-
http://search.labs.familysearch.org/recordsearch/start.html#p=collectionDetails&c=fs%3A1408347
LDS site also has some extracted details from birth records 1864-1881 (exact date of birth and parents' names listed).
http://search.labs.familysearch.org/recordsearch/start.html#p=collectionDetails&c=fs%3A1408347

For births before 1864 you'll need to search for church records to see if a baptism record exists.

[hallmark]

The 24 Church Parishes are; Aughavas, Annaduff, Ballinaglera, Ballymeehan, Bornacoola, Carrigallen, Cloone, Clooneclare, Drumlease, Drumreilly Lower, Drumreilly Upper, Drumshanbo, Fenagh, Glenade, Gortleteragh, Inishmagrath, Mohill, Killasnet, Killargue, Killenummery, Kiltubbrid, Kiltoghert, Kinlough, Oughteragh.

So it looks like your Inch/Inish is a 'version' of Inishmagrath...