Joseph Leman/Lehman/Davis Update---DNA

          I want to bring you up-to-date on the attempts of my first cousin, Frank Davis, and myself to determine just whom Joseph Davis's father was. Joseph, you might recall, was the lineal ancestor, actually Grandfather, of my mother, Naomi (Davis) Holt. We know that Joseph's mother was an Irish lass named Agnus Leman.  (The name has been spelled several ways: Leman/Lehman, Leeman.)  She was born c1820 somewhere in the Emerald Isle.  We also know she had a son, Joseph, born c1840 who stated in the 1880 census that he was born in Pennsylvania. Where?  To date, no one knows. Nor does anyone know whom his father was.  My grandfather, Albert Hooker Davis, always said his grandmother's name was Agnus Lehman/Leman/Leeman.   He never mentioned a grandfather, and I never thought to ask.  
          Enter DNA testing. DNA testing requires a direct line male descendant in order to acquire the same DNA as Joseph's, which is exactly what Frank Davis, Joseph's Great Grandson, is. I am also a Great Grandson but through my mother so my DNA wouldn't get it done. When the results came in, low and behold, not Davis, nope, but Boyd.  Boyd???  Where the heck did that come from?  Joseph's father, obviously.  Or so we thought. The results were 36 markers exactly and 1 was not.  Bingo, 99.9% certain Joseph's father was a Boyd. Well, maybe.
          Months later, after searching for Boyds, another match came in.  This one with 37 markers right on, and  an absolutely perfect match, none of this minus 1 business. Perfect fit, but the name is Hamilton. Here we go again. The Boyd is a few generations back---probably. I have big questions about her pregnancy.   1) When did Agnus arrive in America, and was she pregnant when she arrived? I don't know. 2) Did she get pregnant in Ireland or America? I don't have a clue. If in America, where? Pennsylvania? I really don't know.  I need to know where and when she lived near a Hamilton in late 1839 to have a prayer of finding Joseph's father.
          I am assuming she became pregnant here in America. Ok then, where was she living in late 1839?  Where there any Hamiltons living close by? There is some question about Joseph's exact birth date since the 1840 census gives only male, head of household names, unless the female was the head of household.  In the 1850 census (when finally everyone is named) Agnus is living with her to-be husband, Samuel Davis, in Middlesex Township, Butler County, Pennsylvania, and is listed as Agnus Leman, single, born in Ireland.  No Joseph in sight.  In fact he doesn't show up until the 1880 census living next door to his mother, Agnus and her husband, Samuel Davis in East Deer Twp, Allegheny County, PA.  As an interesting aside, in 1850 she is listed as Agnus, in 1860 and 1870, she is listed as Nancy and in 1880 she again is listed as Agnus. She died in 1881 and is buried as Nancy.
       By then, Joseph had married twice, first to a young lady whose name, (I think but have no proof) was Susan Potts, who died, possibly during the birth of Joseph's oldest daughter, Laura. He then married Sarah Ann Kennedy in 1869 and had four children by her.  Interestingly, in 1869, his Father-in-Law, William Kennedy, in his Bible, listed his name as Joseph Leeman (sp). In the 1880 census of East Deer Twp., Allegheny County, Pennsylvania he was calling himself Joseph Davis.
         I put all this in an earlier blog hoping to get a little help from an interested reader. I'm again calling for your help. The DNA data clearly establishes that his father's surname was Hamilton. The only thing I know to do is assume that Agnus got pregnant in Pennsylvania. The DNA Hamilton family whom Joseph matches have a long history of living in Pennsylvania.  Indeed, in Western Pennsylvania. 
           My guess is Joseph was an out-of-wedlock child, born in Allegheny County, Pennsylvania, father ---- Hamilton, mother, Agnus Leman. He obviously was farmed out, possibly to relatives on either side, somewhere in Allegheny County in 1850 because he doesn't show up with her in the 1850 census when she is living with Samuel Davis.
         He married Sarah Ann Kennedy in 1869 and his first child in this second marriage was Martha Bell Elizabeth, born 23 October, 1870. She was followed by Amy Nancy, Anna Theresa and Hooker Albert aka Herbert Albert. The last two are  not mentioned in the Kennedy Bible.The birth information on his new family is listed in his Father in Law William Kennedy's Bible, and the 1880 census.   I doubt he lived very far from his mother at any time from his birth in 1840 or early 1841 until her death in 1881 in East Deer Twp. (or Tarentum) Allegheny County, Pennsyvania.
         Where oh where was he in 1850, 1860 and 1870? Leman immigrants from Ireland show up in Allegheny, Butler,and Armstrong Counties during those years. I really would like your help in finding our Hamilton relative.