I have an Exhaust fan with 3 phase (415v/50Hz) connection. How can I switch on & off this fan. I have a DDC controller with one relay output to control this fan. Which device I need, to connect my control to my Fan.

You can use a contactor or just a standard 3 phase disconnect depending upon how you want to control it. The site below is informative for DCC operation. Just make sure the contactor is aligned with the DCC control factors and if you want to get deluxe you can go variable speed. This actually needs to be calculated in the field using the original diagrams provided for the system so as not to cause interferences with the rest of the systems controllers or the main logic processor panel.

The easiest way I have seen would be a 3 phase disconnect, however if you want to be able to control this fan with a simple 115VAC switch then you could use a 3 phase motor starter with a 115VAC coil on the contactor. I would lean towards the motor starter as most have a phase protector to prevent the motor from single phasing in the even that you lose one leg of your 3 phase power. This is how I would, and have, installed 3 phase exhausts.