There isn't one single ancient university solely dedicated to Ayurveda. The tradition of Ayurveda developed and was taught in various centers of learning across the Indian subcontinent over centuries. These weren't universities in the modern Western sense, but rather gurukuls (residential schools) and other institutions where knowledge was passed down through oral tradition and apprenticeship. Many prominent medical texts were created and studied in these locations.
While specific names might be attached to certain historical periods or schools of thought, claiming any one of these as *the* ancient university specialized in Ayurveda is an oversimplification. The knowledge evolved and spread through a network of scholars and practitioners across different regions.