Oscar

In the prologue, gangster Angelo "Snaps" Provolone promises his dying father (Kirk Douglas) that he will give up a life of crime, and instead "go straight".
A month later, Snaps awakes at his mansion and begins his important morning. He has a meeting with several prominent bankers, as he hopes to donate a large sum of cash and join the bankâs board of trustees, thereby having an honest job and keeping his word to his father. Anthony Rossano, Snaps's young, good-natured accountant, arrives at the mansion and tells his boss that heâs in love, asks for a 250% raise, then tells Snaps the true love he speaks of is actually "Snaps's daughter." Snaps is furious, does not want his daughter marrying Anthony and goes to talk to his daughter, Lisa.
Lisa is the only child of Snaps and Sofia, a spoiled daughter whose dreams of seeing the worldâs great sights run into a roadblock because of her overly protective father. Wishing to move out of the house, she lies to her parents (at the suggestion of the maid, Nora) and claims to be pregnant. Snaps, believing the father to be Anthony (as he wants to marry "Snaps's daughter"), is shocked when Lisa says the father is Oscar, the former chauffeur who is now serving overseas in the military.
Things get even more complicated when Anthony learns that Theresa, the woman he fell in love with, is not actually Snaps' daughter as she had claimed to be. Before Anthony can catch on, Snaps tricks him into agreeing to marry his actual daughter, Lisa, who is supposedly pregnant but without a husband. Both Lisa and Anthony are unhappy at the hasty arrangement, and the pair luck out when Lisa falls in love with someone else: Dr. Thornton Poole, Snaps' dialectician, whose frequent world travels appeal to her adventurous nature.
Meanwhile, local police lieutenant Toomey is keeping an eye on the mansion, believing that Snaps is meeting with Chicago mobsters soon. Also watching Snaps is mob rival Vendetti, who, too, believes that Snaps is meeting Chicago mobsters. Vendetti plans a hit on Snaps in the early afternoon while Toomey plans a raid at the same time to catch Snaps red-handed.
While Anthony seeks out Theresa, Snaps meets his mansion's new maid, Roxie. As it turns out, Roxie is an old flame of Snaps, and the pair talk memories and the life that never was. Theresa comes to the mansion and is revealed to be Roxie's daughterâwho was actually fathered by Snaps long agoâmaking Snaps her dad after all. The impromptu celebration of both his daughters' engagements is cut short by the arrival of the bankers. During the meeting, Snaps senses the bankers are giving him a raw dealâthey don't intend to give him any actual influence in the bank's operations, despite the money he's willing to invest. The meeting is interrupted by police officers and Toomey, who is embarrassed to find no money or gangsters present on site. He leaves the mansion just in time for Vendetti's car full of armed men to crash right outside. Toomey smiles for reporters and arrests the men.
With the realization that he'd rather deal with gangsters and gunmen than "respectable" bankers, Snaps decides to abandon his short-lived honest ways and return to a life of crime (looking skyward and admitting to his father, "Sorry, dad... I did the best I could"). The final scene of the movie shows a double wedding for both his daughters. Oscar himself finally appears and objects to Lisa's marriage, but he is carried off by Snaps' men and the weddings end happily.

Question: Who does Snaps believe is Lisa's baby's father?
Answer: Anthony