Welcome.
So you have a fan (unknown voltage and current) powered by something and controlled by a mystery Arduino board through a unknown driver.
How will all this unspecified hardware be powered?
So you see that there is some information that you need to gather before you start (not even counting the blynk thing).
First get the stall current and rated voltage for the fan. Then you can find an appropriate driver. Shown is a typical MOSFET driver for a DC powered fan motor.
An AC powered fan would use a different driver, like a relay (mechanical or solid state).
You seem to have ignored the request that you read the how to get the best from the forum thread. Now would be a good time to read it. It will save time later.
What will you use for the timing? Delay(millis())? An RTC? That Blynk thing?..