There is one possibility where "at this occasion" could be used. For example, if you're talking about a wedding being "a happy/joyous occasion".
Let's say the best man is making his speech and he starts talking about a time in the groom's childhood when he did something very embarrassing or stupid. He might get halfway through it and say
"Anyway, I don't want to talk about it at this occasion..." with "occasion" meaning "the occasion of the wedding".
How about during a meeting when someone tries to divert the agenda to an irrelevant topic? Can we use 'I don't want to talk about it at this occasion' in response?
No. A business meeting doesn't really fall into the category of an "occasion" in that regard. The definition I was referring to in "a significant event" or a "large or important social gathering".
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