Every time I write this phrase I have the same doubt.
This is a reminder about/ on the meeting we'll have next Friday.
Which of the prepositions is the correct one?
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Based on the specific example you have used I personally would not use 'on', try to picture the sentence in a different way. I know sometimes that small exercises like this can clear up problems with prepositions. Imagine if the sentence was thus:
This email is to remind you about the meeting next Friday
you could also use the word of in place of the word about, but if you use the word on
This is an email to remind you on the meeting next Friday
The sentence not only ceases to make sense, it also sounds awful.
Thus the sentence...
This is a reminder about the meeting we'll have next Friday.
...is what I would suggest using in future.
My feeling is that prepositions should match those of the verb the noun draws its meaning from to remind someone of something or about something (see definition here).
First of all, I am not a native speaker. However, looking into some reliable tools for the English language the answer seems quite "tricky".
She wrote a reminder about the meeting in her calendar.
But yet again, the results from the Google NGrams show an irrelevant number of occurrences of "reminder about" or "reminder on" compared to the widespread "reminder of".
Based on those results, I would say that when it comes to written language "reminder of" might be definitely the safe and good option, although "reminder about" could be used in spoken English, especially the American one.
Hope someone could validate this interpretation.