How would Jaime treat a child not from Cersei?

If Jaime had been removed from the kingsguard by Robert and presumably married off to some lady, how would he treat children born from that relationship? (Imagining that Cersei doesn't kill them as babies)

He's apathetic most of the time to Joffrey, Myrcella and Tommen but there is some inkling that he does care about Myrcella and Tommen at least