Does your father have a brother?
11% is the lower end of the first cousin range 8-18%... Your half brother should be matching at at about the 18% to 33% range.
My highest DNA match is 8%, and that’s a first cousin once removed... The daughter of one of my first cousins. I contacted her because she didn’t really fit in... When I checked ‘thru’ connections on Ancestry she came up as a fifth cousin on my father’s side of the family... Turns out she’s also the daughter of one of my moms nephews... And she was born out of wedlock.
We had a very cordial email conversation going one. Her father was dead, but he had couple of sisters who were still alive... I contacted them and they weren’t interested in making contact with her. Apparently they were aware of this woman, but they had no interest in meeting with her.
That comes under the ‘family secrets’ section of DNA... Sometimes, the family likes to keep their secrets... Secret.
My own father was born out of wedlock and I managed to find his mother (after she had already passed) whom he had never met, and then we connected to his first cousin who was very happy to meet with my dad... They met, exchanged info on my dad’s mom, my dad went to her grave, etc.
Me and my dad got lucky... His mother and her family make up a big piece of our DNA pie. My dad and I are from Canada and his mother lived out her life in the United States... It was all very nice for my dad’s first cousin to help us out. My dad passed in 2016 so it was also nice that he could at least know of, and about his mother before he died.
Sadly that isn’t always the case.
Does your father have a brother?
Yes, two. My parents never told us we had three half-brothers. We were told they were our cousins. That’s under the family secrets. Our last surviving aunt spilled the beans after my parents passed away. It was only a secret to us; but it was on a paper genealogy compilation from many years ago that we never saw, So she confirmed it. I guess getting divorced wasn’t cool in 1943. Thanks very much for the informative reply.