The phrase our today's meeting is commonly used in Indian English, even though other dialects of English frown upon it. The mentioned examples in the comments of our today's specials and our today's speaker will, I think, sound off to many speakers, but possibly not as much as our today's meeting.
Why is "our today's meeting" wrong? - English Language & Usage Stack ...
Question: What are the origins and history of using on tomorrow, on today, and on yesterday ** (which in standard Englishes are just tomorrow, today, and yesterday)? Examples: US Journal of the Senate (2006, all bold font added): ORDERS FOR ADJOURNMENT UNTIL 9 A.M. ON TOMORROW ...
american english - Origins and history of "on tomorrow", "on today ...
Neither are clauses, but "today in the afternoon" is grammatical (adverbial phrase of time), while "today afternoon" is not. I would also suggest "this afternoon" as a more succinct and idiomatic alternative to "today in the afternoon".
word choice - 'Today afternoon' vs 'Today in the afternoon'? - English ...
In old books, people often use the spelling "to-day" instead of "today". When did the change happen? Also, when people wrote "to-day", did they feel, when pronouncing the word, that it contained two
Change from to-day to today - English Language & Usage Stack Exchange
I think it is a good question. When there is yesterday morning and tomorrow morning, why have an exception for this morning (which means today's morning)? Yes, idiom, but I actually do like idiomatic extensions like these - as long as everybody knows what is meant and no grammar or semantic rules are violated...