I have a book that says "we use present perfect for something that happened in the past without a specific time and still continue until now". Then what should I use if it happened in the past with a specific time and still continue until now?
It's better to consider that the present perfect represents a completed action that could have taken place at any time in the past, right up to the present. If you say
I have seen that movie
I know that you've viewed that movie at some time, but I don't know exactly when. It could have been three days ago, or you could mean that you have just seen that movie, having walked out of the theater moments before.
If you're talking about a singular completed action, then it's over and done with, and it can't continue until now. If you want to talk about ongoing action, you may use the present perfect progressive:
Q: Did you do your homework?
A: No, I have been watching television.
You started watching television at some past time, but I don't know exactly when, and I don't know when you stopped. It could have been any time after you started, including right up to now.