The earliest known GA Logues to have migrated to AL were Jasper J. Logue (real name thought to be Joseph Jackson Logue) and his brother, W. W. Logue.
Jasper was born about 1820 to Sarah and William Logue of Jefferson county, GA.Sarah had previously been married to Jeremiah Warner, but he died circa 1816.After William Logue died in 1823, Sarah and her boys moved to Bibb county, GA, by 1830, and by 1840 Jasper was head of household in Marion county, GA.Sarah was apparently living with him.Jasper is found there again in 1850 but was living in Lowndes county, AL, by 1855, per the AL state census.Brother W. W. Logue was apparently living nearby in 1855.W. W. Louge (sic) lived not far away from Jasper per the AL state census.
Sarah Logue was living with son, Benjamin Warner, in Barbour county, AL, in 1850.If I'm not mistaken, W. W. Logue was living (unmarried) with Jasper Logue's family in 1870.
Likely your Logue ancestors descend from Jasper . . . OR Samuel Logue, an Irishman, who was in Mobile county, AL, by 1850.