You have some very interesting Information. I show William Reily b17Dec1842 in Paradise d8April1919 at York, PA. He was married to Jame Pouch b18Dec1857 d16Feb1902 at Spring Grove, PA. One of their 7 children was Amelia Rebecca Riley b1884 d1927 m26May1906 to Irwin Franklin Schauer son of John Schauer. Amelia and John had a son Eugene Alexander Schauer b1907, York, PA m29Nov1928 at York, PA to Claudia Lanningham b29Nov1907. They had daughters Yvonne Elane Schauer b20Dec1929 at York, PA and Norma Jean Schauer b17Oct1934 at York, PA.
Perhaps your Anna (Annie) is the Amelia Rebecca Riley above?
My records show that William Reily later changed the spelling of his name to Riley.
My evidence that the father of Catherine is John Klinepeter comes from the will of Elizabeth Smith probated 1851. From census and tax records it may be that this Elizabeth was also the widow Heiner. I have a copy of the will that I made at the York County Court House. Catherine Baublitz is buried at Pleasant Hill Dunkard Cemetery's old section in what is now Jackson Township formerly Paradise Township. One of her daughters of her marriage to Michael Baublitz, infant children of John Reily (William Riley's older brother) and a Heiner that was a veteran of the war of 1812 are buried near her. Elizabeth Smith also indicates that the father of her grand children, the children of Washington Reily and her daughter Catherine are John, Elizabeth and William. Washington Reily disappears from about 1843 to 1870 and shows up in the 1870 census living with his son John.
Still, I would like to know more about how this Eli Riley seems to be a plausible father for John, Elizabeth and William. Catherine could very well have gone off to Indiana some time after 1842 and then returned in time for the 1850 census. It is also possible that Eli was Washington's father or perhaps Washington's full name was Eli Washington Reily. Please fill me in with more details or else put me in touch with your online source.