No idea for cats but I used to do a ton of carp fishing in ohio. My 4 best patterns were:
1) brown wolly bugger because one of carps favorite foods is crayfish.
Drag it by them while they are tailing and hold on.
2) Beadhead
They eat a lot of nymphs and a beadhead will get it down on the bottom in front of them when they are actively feeding.
3) Dandylion Fly
Yeah, seriously, and no kidding. Size 12 hook with a small amount of pure white hackle tied at the top. Wrap the body well with black thread to get a bulge near the curve of the hook to mimic a seed. They eat the heck out of those in the summer and it is a good way to dry fly fish for them.
4) Mayberry Fly
Size 12 or 14 hook wrapped in black or dark purple chenyle (probably spelled wrong) and have a piece of feather stripped down to the central vein that will come out one side or the other to mimic a stem. Then find a few mayberry trees along the river or lake that are dropping fruit. The carp will be stacked up underneath looking for a treat.
Good luck and post how you do. I haven't fished for them in years. There aren't that many in Montana but I used to have a ton of fun catching them in Ohio. My favorite were the grass carp that would actually jump.
flyfish59102