Question: Can I come to your office day after tomorrow?
Answer1: You can come at anytime.
Answer2: You can come at anyday.
Which one of the above answer is correct?
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Anyday is not a word - it's always any day, two separate words.
Any day means whatever day you or someone/something else wants. It might also mean any time if a time hasn't been established, but if one has it does not alter it.
A: Can you come over at noon during my lunch today?
B: I can't make it today. Which day after today is good for you?
A: Any day.
B: Ok, cool. (B expects A to arrive at noon on whichever day A chooses)
Also, any day is not a time expression and doesn't need at (on would be more correct but also optional). At is optional with anytime.
I want to come over at 3pm. (at not optional).
I want to come over [at] anytime you want.
I want to come over anytime you want.
I want to come over [on] Tuesday.
I want to come over [on] any day.