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Offshore company in a different country, do I need a company in my country?

If I have an offshore company in Cyprus for example, do I still need to have a company in my current country?
Usually no, you don't need that.

Let's say I will get paid on my offshore bank account and I cashout in my country at ATM, is there any issue?
No issue but you will have to pay tax from the money you earn and even take out at the ATM's