“Highbred”(often spelled “high-bred”) is occasionally used to label animals with superior ancestry. Snobs used to refer to members of the nobility as “highbred.”
But this rare word is often confused with “hybrid,” which describes plants, animals, and people that are the product of mixed heritage.
The offspring of a line of prize-winning dogs would be “highbred,” but a dog could be called “hybrid” if its ancestry were mixed. It might be a prizewinner, but it might also be a mutt. Except in a context where “highbred” is routinely used in this technical context, stick with “hybrid.” It’s almost certain to be the word you need.