The correct answer is “at”.
“At” is the most common preposition to use with the verb “go” when referring to a specific time or place. In this case, the speaker is saying that there is no point in going to a particular place at a particular time.
The other options are not as idiomatic in this context. “Off” is used to refer to a departure from a place, “on” is used to refer to a journey or a period of time, and “in” is used to refer to a location or a period of time.
For example, you might say “I’m going off to work now” or “I’m on my way to the store” or “I’m in the kitchen”. However, you would not say “I’m going off to the store now” or “I’m on my way to the kitchen” or “I’m in work”.
In the context of the sentence “There is no use going there at this time”, the speaker is saying that there is no point in going to a particular place at a particular time. The most idiomatic way to express this is to use the preposition “at”.