Father's DOB of 1783 plus 18 y gives estimated DOB of 1801.
I found one record for a Patrick Agnew Born in Ireland, 3 records for New Hampshire Census 1880, 1900 and ----, one newspaper clipping for a marriage in PA. But nothing with his father. All on Ancestry. 14 records total on FS if limited to South Carolina,10+ pages if just searching United States for 1800's
Sources
Acknowledgement
This person was created through the import of JDS_09_17_10.ged on 09 February 2011.
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DNA Connections
It may be possible to confirm family relationships with Patrick by comparing test results with other carriers of his Y-chromosome or his mother's mitochondrial DNA.
However, there are no known yDNA or mtDNA test-takers in his direct paternal or maternal line.
It is likely that these autosomal DNA test-takers will share some percentage of DNA with Patrick: