I assume you mean the High Middle Ages? It really depends on the animal. Cats weren't common domestic animals since many considered them to be evil. However, an English law regarding rights to shipwrecked loot says that, so long as no man nor cat were alive, anyone was free to do with the loot as they wished. Cats were mandated onboard merchant vessels, probably to eat rats, but that's conjecture. (Disclaimer: Cannot provide primary source for cats mandated aboard ships, but if any actual historian knows where to find more information please add to this).

Dogs were kept as hunting pets primarily, and as such fed hunting scraps and dinner scraps (the latter might also go to hungry beggars as well). Burghers in large cities might have a pen behind their home, with a few chickens (who ate feed) and a pig (typically given free reign on the streets to eat trash). Cows would typically eat grass.

Hope this helps! I'm on mobile so I apologize for this reading like a rough draft. Have a good one!

Source: Morris Bishop, The Middle Ages (1968)

None of the manners books in Rickert's The Babees' Book: Medieval Manners for the Young mention dogs in the dining hall, so it was probably rarer that we picture to give a slice of mutton to a hound. Dogs were primarily fed on dogs' loaves, whole wheat with cheaper grains. It was an unusual expense to buy an old horse to slaughter to give "some sick hounds" meat: they were living largely vegetarian, which dogs can do. It also made them the more eager in the hunt, since they got part or all of what they caught.

Actually, people did keep cats in the house, primarily for pest control but they could also be regarded as pets. Famously, there is the poem by a 9th-century monk to his cat Pangur Ban. The [poem is here] (https://medievalfragments.wordpress.com/2013/02/22/paws-pee-and-mice-cats-among-medieval-manuscripts/), as well as a 15th-century manuscript with cat paw prints on it and another stained with cat pee! [See here for a decent discussion] (http://www.medievalists.net/2013/08/11/pet-care-advice-from-the-middle-ages/) of medieval pets that includes a little about how to feed dogs.

I'm honestly surprised nobody as cited this book, but there is a monograph named Medieval Pets by Kathleen Walker-Meikle. I believe it's based on her dissertation research and it's great.

As far as cats go, the author makes the observations that they are harder to trace in the accounts since they forage for their own food (regardless of whether or not they are indoor or outdoor cats). She does, however, note one record that states that money had been allocated for cheese for the cat, but that may have been for mice.

In general, Walker-Meikle argues that pets were given food that was as high a quality as the owner could afford. For dogs, "...the staples were bread, often of a fine quality, and milk, occaisionally with meat." This is corroborated in the Canterbury Tales (one of her main sources as she seems concerned with England) and household accounts. Indeed, in these accounts panes pro canibus (bread for dogs) is explicitly mentioned. She also has information for how birds and monkeys were fed if you're interested.