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Salmon / Sammon: Descendant of bradán' (diminutive of brádach, spirited; also a salmon) was a rather scattered surname in Co. Roscommon, it seems to have been an alias for Ó Bradagáin, which see. Salmon, as an anglicised form of this surname, dates back to the year 1555; and Salmon, of course, suggested Fisher [Sloinnte Gaedheal is Gall]
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You are in luck ... Timothy & Winifred Salmon baptised a daughter during the only year a Killucan priest bothered to record an address in this parish (so you can be confident this is where your ancestor Timothy Jr was born too).
Timothy Salmon Sr. aka Tadhg Ó Bradagáin began raising a family in the townland Tullyleague. Just west of Carrick-on-Shannon, Tullyleague is technically in:
The house I believe they lived in (TBC) is mapped here as a cow-house in 1857. No longer extant by the end of the 19th century.
Thady Salmon was married to Winifred Feely ... her actual name would have been Deirdre Ní Fhícheallaígh (Winifred was an Anglicization of Deirdre).
Baptised in RC Killucan (civil: TUMNA):
Margaret Salmon bap. 10-Mar-1816 (godparents: Michael Healy & Mary Lauder / Lawder)
Thaddy Salmon Jr. bap. 5-Feb-1823 (godparents: William Lynch & Catherine Smyth)
It looks like they moved west in the direction of Frenchpark shortly after that...
Baptised in RC Loughlynn (civil: TIBOHINE):
Catherine Salmon bap. 9-Sep-1830 (godparents: Hugh Foley & Brigid Salmon*)
Bernard / Bryan Salmon bap. 8-Oct-1835 (godparents: William & Sarah Johnson)
John Salmon bap. 12-Apr-1838 (godparents: Thomas Salmon & Anne Flanagan)
RELATIVES IN KILLUCAN (near Carrick-on-Shannon)
In 1818, Thomas Dolan & Anne Davis invite both Timothy Salmon and Winifred Feehily to godparent. They must have been very close (possibly sharing the same farm/house). There are no other records for this couple, however... in 1857 Peter Dolan of Lodge holds land at farm #9 Tullyleague along with a roadside "office" #9a (an old house being used as a farm outbuilding/ cow-house). Odds are high that this was the home of Tom Dolan, quite possibly with Thady Salmon attached.
Given that Salmon was such a rare surname here, you might also consider John Salmon of Knockroe as possibly related. See John Salmon & Anne Murray;
RELATIVES IN LOUGHLYNN (near Frenchpark)
*Brigid Salmon (presumably Thady's sister) married Edward Sarsfield in 1837 and baptised one child later that year.
No more records for either couple, which suggests they probably emigrated soon after as well.
Then, as you say, Timothy Salmon migrated to England in June 1846.
Let me know if you see any of those other names mentioned turning up as neighbours in your UK records.
The only other Timothy Salmon on record in Co Roscommon did not emigrate ...
Timothy Salmon (1796-1876) & Margaret Beirne (1806-1886) baptising in the RC parish of Aughrim were of Breanletter, Ballyfermoyle (civil parish of KEADUE).