The Morgan Stanley investment banker accused of stabbing a New York cabby during a dispute over the fare to his Connecticut home yesterday asked a judge to toss the case, claiming the hack told conflicting stories to cops on different days.

A lawyer for W. Bryan Jennings noted that Mohamed Anmar told cops Dec. 22 that he had just been stabbed in the driveway of Jennings’ home — but then a week later told a detective he had been stabbed at least a mile away on Boston Post Road.

And Anmar told cops a week after the incident that Jennings had drunkenly yelled “You should go back to your country!” — but had not made that claim when he first spoke to police on Dec. 22, according to a motion by Jennings in Stamford Superior Court.

These discrepancies, and the fact that Darien police failed to inform a judge about them when they sought an arrest warrant, means that “the arrest warrant is fatally defective and the case should be dismissed,” Jennings’ lawyer Eugence Riccio told The Post.