I have server with Xeon E3 CPU 4/8 cores. There is a virtual private server assigned to this computer and it takes 100% of one core permanently. So 1 of 8 is maxed out permanently. I want to ask if this state can cause any hardware issue over the weeks or so? WOuld this be fixed if i assign this VPS only like 70% of a core?
It shouldn't cause any hardware issues. Depending how you have it set up and which visualization technology you've chosen, you can spread the load across all the CPU cores but not let it exceed the total of 1 core at any given time. Processors usually don't go "bad" so if you're asking if the constant use of a core can cause physical/hardware problem, it's not very likely at all (I wouldn't believe anyways).
No, it isn't going to matter unless you have other VPS users on that server. They are monopolizing the core and other users won't be able to. Hardware-wise, no. Everything will be fine.