The phrase "and a wad of" is correct and usable in written English.
It can be used to describe a quantity of something that is gathered or compressed into a lump or mass, often referring to cash or paper.
Example: "He pulled out a wad of cash from his pocket to pay for the dinner."
Alternatives: "and a bundle of" or "and a pile of".
I had a wad of Indian and a wad of Mexican and a wad of Chinese (not just Takeout Chinese, either) and a wad of Japanese and a wad of pan-Asian and a wad of Italian and a wad of Middle Eastern and a lot of menus I found unsortable.
It's inside her medicine closet along with toiletries, her family's passports and a wad of cash.
Once, Ben Ahmed walked into the lobby of his building and saw a man holding a bag of drugs and a wad of cash.
He pulled the door open a few inches, and then it stopped, jammed against an empty cardboard box and a wad of hanging coats.
In Lorde's case, "a kindly woman" comes bearing "a soft sleep bra and a wad of lambswool pressed into a pale pink breast-shaped pad".
There, she tries to convince him to buy a warehouse full of memo pads, giving him cartons of cigarettes, champagne, and a wad of money.
Let's go in and get him!" Maddy gets out of the car and pulls a wad of lion's mane from a thorn.
He bought us season passes to a local waterpark, where he spoke loud, boisterous Farsi and flashed a wad of cash wrapped in a rubber band.
Don, irritated by the Joan situation and the lack of progress in the Jaguar pitch, blew up at her and threw a wad of bills at her head, humiliating her in front of Ken and Harry.
I took off my wetsuit, and when I got to the stand where I had borrowed it I saw Papazian, who was talking on the phone and had a wad of cotton in his ear.
The brother, Semo (Nurettin Celik), turns out to be a pimp from the old school, which means that when he's not swaggering about and flashing a wad of cash, he's slapping his women upside the head.
