Is this superstition/proverb from UK or US? "Derby horse pup from derby horse." Do you know this superstition/proverb ?

I don't think I'm understanding your question correctly. However, back in 2015 talk show host Jimmy Fallon had part a segment in his show (USA) which he used a bunch of puppies to try to predict which horse would emerge victorious in the Kentucky Derby. The bit involved puppies racing to a trough of food, and each pooch corresponded to a different thoroughbred. As it turns out, the puppy representing American Pharoah won the contest and on that Saturday, the actual American Pharoah won the Kentucky Derby.

Uncle Pup a 5 year old gelding per Horse Racing Nation.

Never heard of it and had to Google it and found it was a horse bred in Oklahoma.

Though it could have made its way to the UK given I know an American who ran his American bred horses in the UK and sold one to the Prince of Dubai.

praying that my heart just won't end