If i cast and copy Rousing Refrain, will the copy go in exile with 3 time counter on it?

Everyone else has told you the copy just goes away. That's the correct useful answer, for all practical purposes. But.

If i cast and copy Rousing Refrain, will the copy go in exile with 3 time counter on it? ...the overly literal answer to exact the question you posed is "yes it does".

Technically the copy does exile itself, and it does get three time counters--then it ceases to exist as a state-based action just before anyone gets priority.

I cannot actually think of any way this matters.

Even if you had one of the rare effects that can touch exiled time counters, and could somehow pull one of those out in the middle of the copy resolving (so it could act before the copy stopped existing), you still couldn't target the copy. Effects like that all say "exiled card" or "suspended card." The copy is suspended and exiled, but it's not a card.

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