I'm going to join in on Genea-Musings' Saturday Night Genealogy Fun. This week the topic is your father's mother's line. I'll answer the questions one by one --
1) What was your father's mother's name? Her birth name was Mary A. Siegler (and I haven't found out what the "A" stands for). Over the years she was called Maria, May, and Mae -- the last was the name we knew her by. I've wondered whether she adopted that spelling from Mae West, with whom she rode the bus when she was a young working girl (as was Mae West).
2) What is your father's mother's patrilineal line? That is, her father's father's father's ... back to the most distant male ancestor in that line? Mae's father was George Siegler, who was born in Lohr, Bavaria, on October 22, 1869, and who came to the U.S. when he was a teenager. He married Matilda Hug, born 1879 in New York City. George's father was Nikolaus Siegler, born 10 March 1825, in Lohr, Germany; he married Maria Josepha Vogel in 1869 (three months before George was born, interestingly . . . ). Nikolaus Siegler was a stone mason. Nikolaus' father was Balthasar Siegler, birth date unknown; he married Margarethe Siebelitz on May 26, 1817. That's as far back as I can go at this point.
you identify male sibling(s) of your father's mother, and any living
male descendants from those male sibling(s)? If so, you have a candidate
to do a Y-DNA test on that patrilineal line. If not, you may have to find male siblings, and their descendants, of the next generation back, or even further. Unfortunately, my grandmother had no male siblings who lived. I'm confident that she had a brother named Nicholas, born in 1899 and who died at the age of three months. I believe there was another brother in there also, but I can't put my finger on the record that leads me to think so. So all we have is Mae, and her sister Dorothy, who was born many years later.
At this point, that's all I know. Probably George Siegler had siblings, but I haven't come upon any records of them yet. But we will keep looking!