“At this time” vs. “at that time” vs. “at the point of time”

They’re all just roundabout ways of saying things we usually do in a single word…

at this time = now
at that time = then
at the point of time = when

I don’t much like at the point of time. Obviously, I normally use when anyway, but it’s usually at the point in time if I have to use the longer form. Except in “scientific” contexts like at the point of time T (that’s almost 7000 of them in Google Books). I don’t mind that usage so much, but I really don’t like this type

One, therefore, arrives at the position where, if there were successive partial losses which are unrepaired at the point of time when the cover terminates, the measure of indemnity has to be assessed by reference to the depreciation at that time.

Here’s a chart showing that in has been standard usage for decades…

The shift in preference is far more marked than the chart would suggest. The vast majority of modern usages are that “scientific” context. Most of the rest are (like my fully-quoted example) legal contexts.

Unless you’re writing scientific or legal texts, my advice is don’t use any of these long-winded phrasings. And if you have to refer to the point, it’s in time unless you’re talking about a specific time T on a graph.