If you've tried multiple different models of PSU and it still clicks, then it isn't the power supply. Look to the graphics card, CPU cooler or case fans for a fan that is hitting something like a piece of wire or a wire tie. Check to see that there is not a wire tie or something sticking into the power supply from the case.
Make a funnel from a piece of paper or thin cardboard, put the small end against your ear and use the large in to move around in the case until you can determine, carefully, where the clicking is coming from. It could be a component on the motherboard itself or a fan bearing. Do you have a water cooler for the CPU, if so, could be a pump noise.
Does the system work normally other than the clicking noise, or are there other issues such as shutting down or not starting involved, or a lack of performance that wasn't a problem before the clicking started?