The expression “fork it over” has a connotation of urgency to it and is often used dramatically during a criminal holdup.
In fact, the expression does have origins in a long-forgotten underworld.
Of course, the phrase can also be employed with humor when asking for a financial payment for goods or services rendered or for the repayment of a loan.
The “fork” in question is a reference to “fingers,” which were the original dinner forks, especially for thieves and other low-lifes.