Hola Oscar :-)
The correct phrase is the second one: "What time did you watch this class?"
(You could also say "that class" or "the class". The phrase is in the past tense and therefore you use "did". You are asking something that is past tense, "what time DID you watch the class" (or what time did you see the class" or "view the class". You use "did" because the class has already happened, it is completed and therefore you need the past tense form of the verb "do". You might reply: "I WATCHED the program last night at 7pm."
The first phrase is incorrect because it is an incorrect mix of tenses. "Do" and "watched" cannot be together in the phrase. Instead, you could say "What time do you (or will you) WATCH that program?" or "What time do you WATCH that online class?" You might reply: "I WATCH it every morning at 9am."
I hope this helps. Please ask if any questions or confusion. Best wishes in your language studies!