Major SPOILERS ahead for Joker!
One of the mysteries in director Todd Phillips’ Joker is whether Arthur Fleck really is the son of Thomas Wayne as his mother Penny Fleck claimed. Both Wayne himself and Arthur Pennyworth said it was untrue and that Penny was delusional, hence her eventual stay in Arkham Asylum. But to Brett Cullen, the actor who plays Wayne, “in my mind, Thomas Wayne put her there.”
Penny Fleck worked for the Waynes thirty years before the events of the film, with Arthur learning that he was adopted by her while she worked for them. Penny had previously admitted to Arthur that she and Thomas had an affair, that Arthur is Thomas’ son, and that’s why she’s been incessantly writing to him so that he could help them out financially. Penny also said she was made to sign some papers requiring her silence on the matter.
Source: IGN.com Joker Actor Confirms That Theory About Arthur Fleck's Past