Step 1: Understanding the Concept:
This question relates to the different sects and cults within ancient Indian religions and asks about the primary affiliation of the deity Vasudeva.
Step 2: Detailed Explanation:
The worship of Vasudeva, who is identified with Krishna and later syncretized with Vishnu, forms the core of Vaishnavism (the Vaishnav cult).
Vaishnavism is one of the major traditions within Hinduism and it conceives of Vishnu as the supreme being.
Let's look at the other options:
Shaiv (Shaivism): This sect venerates the god Shiva as the supreme being.
Baudh (Buddhism): This is a separate religion founded by Siddhartha Gautama (the Buddha).
Jain (Jainism): This is another distinct religion, with its teachings based on the Tirthankaras, most notably Mahavir.
Step 3: Final Answer:
The cult centered around the worship of Vasudeva-Krishna is known as Vaishnavism. Therefore, option (A) is the correct answer.