Speaking strictly of Irish participation in the war between the states, I can think of the 6th Louisiana Volunteers as a notable Confederate unit. (See "Irish Rebels, Confederate Tigers: A History of the 6th Louisianna Volunteers" by James P. Gannon)

Also there was Kelly's Irish Brigade, in the 5th Missouri CSA, led by Joeseph Kelly, who participated in battles in Mississippi and the Atlanta campaign.

Perhaps the Irish participation in the south was not as notble due to the fact that they were not drawn from new immigrant boroughs as they seem to have been in places like New York and Boston.
Another thought may be that CSA units may not have been comprised of newly arrived Irish immigrants, but rather descendants of those who had settled in the south long ago. After all, a great many regions in Virginia (for example), particularly the mountains and the northern neck and middle peninsula, were settled by Irish, Scottish, and English-born people.

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