1. I have gifted him 17th September 2020 a sum of $1000. :cross:
2. I [STRIKE]have[/STRIKE] gifted him [STRIKE]a sum of[/STRIKE] $1000 on 17th September 2020. :tick: with my changes.
[STRIKE]The[/STRIKE] Which one of the above sentence is correct grammatically?
Note my corrections above.
Sentence 1 is unfixable because the word order just makes no sense. You can't gift someone a date.
I have fixed sentence 2 by showing you the correct verb form (simple past) that's used when talking about a specific date. There is no need for "a sum of". Note that, in BrE, using "gift" as a verb is not particularly common. I know at least one person on whom it grates hugely because so many nouns are now being unnecessarily converted into verbs.
I'd
write "I gave him $1000 on September 17 [2020]"
I'd
say "I gave him a thousand dollars on the seventeenth of September [this year]".