MinHeap implementation in Java
Style  


Dead code should be removed. maxSize is never used.  
Be consistent in your style. You should decide wether you use this. If a decision is made you should stick to it.  

Here i would suggest refactor the constructor to  

public MinHeap(int maxSize){
    heap = new int[maxSize+1];
    heap[0] = Integer.MIN_VALUE;
    size = 0;
}  



Simplification  

In the isLeaf() method you basically say if the condition is true, return true otherwise return false


private boolean isLeaf(int position){

    if(position &gt; size/2){
        return true;
    }
    return false;
}



This can be simplified to return if the condition is true.  

private boolean isLeaf(int position){
    return (position &gt; size/2);
}