You want a very small shot shell fired in a rifled barrel. Understand that even at its best you won't get much range but 8-10 feet is possible. I do it with .303 Brit cases modified to fit a .44 Magnum chamber because standard cases are too short to hold much powder and shot. Mine are deadly on snake heads at 6 - 8 feet.
1. Fine shot works best, #9 or smaller, as much as you can get on top of a few grains of Bullseye or Red Dot. I use 3 gr of Red Dot but for your slmaller cases I'd start with maybe 1 1/2 - 2 gr. Bullseye. It's virtually impossible to load enough powder and shot to make it dangerous to shoot but excessively hot charges will blow through the powder wad and do sad things to your pattern.
2. An "over powder" wad of toilet paper packed in tightly with a dowel rod end, use just enough paper to make it maybe 1/8 " thick, works about as well as anything fancier. After it's packed down, drip 4-6 drops of candle wax on the paper wad to weld it more or less together much like an old time fiber shotgun wad.
3. Run your charged cases into a seater die and "crimp" roll the mouth just a tad to give your shot cluster something to grab hold of.
4. Add as much fine birdshot as you can get in and still be flush with the case mouth. (stacked up, over filled shot "round offs" are too fragile for much handling.) Drip another 5-6 drops of melted candle wax over the top exposed pellets to seal them into a more or less solid blob. The pellets easily upset and separate when fired but mine don't pull out when (modest) regular cartridges are fired.
I have a tentative plan to extend the length of my shot column by placing a rolled paper sleeve inside. I'll make it long enough to completely fill the cylinder and use the same melted wax treatment to hold everything together before firing.
I don't have a Phd, not even a BA. But I do have a DD214.
Common sense is an uncommon virtue