This is my grandmother's great-grandfather. The information I have about him comes from a book titled "Randall Family 1800-1980". Are you familiar with this book? I do not see where this book is sourced, and indeed parts of it seems to be credited to family hearsay. But it is all the information I have so far. It says that his father was Jacob James Randall. All it says about Jacob James Randall was that he "came to Canada from Ireland". He had 3 sons Felix, Joseph and James. It says they all three moved to the U.S. when they were grown, James to Wisc; Joseph to Illinois; and Felix to Missouri.
James Jacob Randall was born in 1820. Married Hannah Ann Soule August 27, 1846 (or 47) in Saulk Co WI/Baraboo, WI. He died 23 July 1893 in Haddam, KS. The book contains a picture of his wife Hannah Ann Soule. It says she was Pennsylvania Dutch and that she was born in Penn. She had two daughters from a previous marriage. Then she and James Jacob Randall had six sons. The book says that James Jacob Randall and Hannah Ann Soule are both buried in Hawks Cemetery near Haddam, Ks. I am from Kansas and I hope to try to find their gravesite soon. I would be very interested in finding out more about these two myself.