If you are using leftover cooked potatoes just don't use anything that is too creamy or wet. This sounds like colcannon cakes but that would never work because mash that you make intending to be mash should be smooth and really creamy
Directions
Baked potatoes are ideal as they are completely dry. You don't need to add liquid; just take the dry mashed potatoes and whatever you are mixing them with and make into cakes
You can fry in oil or butter but butter tends to make them go more crispy and brown
Ingredients
The one in the pic was roasties, swede, cabbage and peas from Sunday lunch mashed together, shaped into cakes and fried in Butter until brown on both sides.
The classic combination is cabbage and onions