Bitcoin backed fiat currency

Generally, fiat currencies have a number on them that identifies one paper note with other. Can a Bitcoin backed fiat currency be used or is in operation?

Let’s say we have gold and their equivalent(approx.) as fiat currencies in the market.

So can it be possible to have a currency in offline market that correspond to bitcoins, so that bitcoins could be more effectively used?

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I’ve deleted my wallet and never backed up my files

I’ve deleted my wallet when I whipped my computer recently and never backup my files. The only thing I’ve done was convert money into bitcoins and it was sitting in my wallet never touched. I reached out to the company that processed my conversion and they provided me with the necessary addresses that were used. How can I recover my bitcoins. Any help would very appreciated. Thank you.

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