You've been fed the usual line about a "crazy ex" who "stops me seeing my kid" that he was "tricked into" fathering in the first place!
It's so so so common.
You only know what he's told you, what he's allowed you to know.
Have you actually seen evidence of the child maintenance payments? The csa letter he recently received? His communications with his ex?
His own health issues don't negate the possibility, even likelihood that he's lied to you about the true situation here.
"he says she lied about being on the pill" again
A - you've only his word for that
B - he's a grown adult, if he's old enough to have sex he's old enough to take responsibility for his own fertility
C - just her getting pregnant is not proof she lied! Contraception fails on occasion. My first pregnancy was a pill failure and I was absolutely taking it properly, hadn't had an upset stomach or any meds that would have interfered. Sometimes shit happens!
If he really believed he wasn't the father he would have insisted on a DNA test not paid cm for a child he's not even sure is biologically his!
"The world seems to be almost entirely populated by batshit-crazy exes."
None of whom are deemed unfit parents - funny that eh?!