He's hinted at having some bad things happen in his past, no mention was ever made of Misfit's dad, and he's just old enough for it to be biologically possible. When Babs asked him, he wouldn't say why he transferred to Gotham, but we know he's not from the city originally. Maybe he lived in that poor Metropolis slum as a kid, got an older woman pregnant, but wasn't actually involved in Charlie's life. Years later, he hears that his old girlfriend and her kids have died in that fire, but a few months later gets word of somebody with his daughter's name in foster care in Gotham. So he moved to be closer to her, but may or may not have ever approached her. Think about, "Charlotte Gage-Radcliffe?" Maybe the hyphen was to remember him by?