API Gateway for blocking api calls
My first point would be that if I want throttling for my API, I would put it in some kind of interceptor. However since this is an interview assignment and for the sake of simplicity I would recreate that as a function call:

public synchronized void create() {
    if(isAccessible()) {
        create(employer);
    }
}


Secondly, I don't think it is a good idea to block with the while-loop you have, when the quota of calls have been made. Instead return a meaningful message that explains why the request was denied. 

With the current implementation you are using the InterruptedException as part of your control flow, which is usually considered an anti-pattern https://softwareengineering.stackexchange.com/questions/189222/are-exceptions-as-control-flow-considered-a-serious-antipattern-if-so-why.

I feel like a simpler solution would be to simply reset the counter every 60 seconds in the Timer class, similar to what you are already doing. Maybe I am missing something, but I don't understand why you are doing the check:

System.currentTimeMillis()&lt;=timer.getElapsetime();


You are already resetting the counter every 60 seconds, so I would just return false in this method.

My last point would that generally the client would be passing Employee (or whatever data needed to create an employee) in the request, so it does not make sense to have Employee as a field. Rather it should be a parameter of the create function. 

If this came as an interview question I would also see it as an opportunity to talk about throttling, and what alternatives there are. For example, maybe checking the rate of calls instead of having a fixed window of 60 seconds would make sense. However that's not that related to this code review.