Assume, someone's reputation within a day exceeds the threshold 200 units.

What will happen to the rest of it?... Will it be considered for the next day to be applied or it will be lost?


No, upvotes received after you hit the reputation cap will not be applied the next day.

From What is the daily reputation cap and how can I hit it?:

The maximum amount of reputation you can earn in one day from upvotes and approved suggested edits is 200. Any upvotes you receive after reaching that number no longer award any points.

You can still earn rep beyond the cap by winning a bounty, accepting an answer, or having one of your answers accepted. Downvotes will also still count against you, but the rep lost can be reclaimed from new upvotes.

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