Billy has a very complicated backstory!
Charlie was 3 years older and the golden child Billy was jealous of.
Wiki just says Billy’s parents put him in care which is an odd decision - why? So you could be on to something there @70isaLimitNotaTarget and Billy is not their joint child. Although (I'm not sure why) but I had the impression Billy was put into care relatively late in childhood, not as a baby?
My gran was born in 1916 and her father, who was away part of that year at war, was always convinced she was the product of a fling by his wife. He always treated her differently to her brothers and sisters, no presents at Christmas etc.
Would they go there with Billy being Teddy’s dad? It's EastEnders, they might!
I don’t know if this is just a careless name change but wiki says
"William "Billy" Mitchell is the son of Stevie and Val Mitchell”
And then further down
“William Mitchell was born on the 3rd May 1959 in London to Stephen Mitchell and Janet Mitchell."
I’m assuming Janet is the correct name, and young Janet was named after her?