I didn't get your question exactly. what do you want to ask?
To extract k-smallest element the time complexity is O(klogn), why?
I have considered the min-heap was already built[which takes O(n) time].
swap the root with the last node and fix the heap of heapsize-1(as we do not consider the last node to participate in heap fix), this will give next smallest element on root.
Similarly, repeat this process 2 time if you want 2nd minimum element and k-time if you want kth smallest element.
Each min-heap fix will take O(lgn) time and there are 'k' such min-heap fixes as we do min-heapfix after every min-extract.