Perhaps you're thinking of a different brand or a particular dog that someone might have called a "Yuengling beer dog" in a humorous context.
Could you provide more information about where you saw or heard this term?
What kind of dog is the Yuengling beer dog?
There's no official "Yuengling beer dog" breed. Yuengling Brewing Company doesn't have a mascot dog, and there's no specific dog breed associated with the brand.