Array-based stack data structure in Java
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There's nothing saying an array-based stack has to have a fixed size. The standard library Stack doesn't have a fixed size, and it's array-based. Same with ArrayDeque, the stack you should be using instead of the Stack class.

Just make a bigger array if you run out of room. You'll want to grow the array by a multiplicative factor to make sure you don't have to resize too often; you want push to be amortized constant time.

public void push(E obj) {
    if(data.length == size())
        data = Arrays.copyOf(data, 2*data.length+2); // +2 in case data.length == 0
    data[++top] = obj;
}


Get rid of the capacity instance variable.

You literally never use it.

Are those checked exceptions?

You declare throws EmptyADTException on two of your methods, which you shouldn't have to do. throws is only necessary for checked exceptions, and EmptyADTException shouldn't be a checked exception. Checked exceptions are for things that might go wrong even if the code is correct, like FileNotFoundException. If someone tries to pop from an empty stack, that's a coding error.

If your EmptyADTException is a checked exception, make it descend from RuntimeException so it's unchecked. Making it a checked exception just bloats any code that uses your stack, and the exception-swallowing catch blocks that result will actually reduce the chances that bugs are found.

Consider throwing NoSuchElementException.

It's what the Java Collections Framework throws for cases like popping from an empty stack. There's also EmptyStackException, which is what the standard library Stack throws, but I don't recommend it. Stack is old, doesn't really fit with newer additions to the Java standard library, and has old design mistakes like built-in synchronization. You shouldn't try to copy it.

Don't use the increment/decrement operators inside of a bigger expression.

Code like data[++top] = obj; requires more thought about what happens in what order than something like ++top; data[top] = obj;.

Don't try to make generic arrays.

    this.data = (E[])new Object[capacity];


This might look like it works, but that's just because type erasure prevents Java from noticing the error. What you're doing here is storing an Object[] in a variable of type E[], even though Object probably isn't E. If you ever do anything that lets Java notice the error, for example

// Inside the Stack class, so data is accessible
Integer[] ints = new Stack&lt;Integer&gt;(5).data;


you'll get a ClassCastException. The correct way to make a generic array is a lot of unnecessary hassle; the best way to go is generally to just make the data variable an Object[]:

public class Stack&lt;E&gt;
{
    private int capacity;
    private Object[] data;


and cast elements when you retrieve them from the array:

public E top() throws EmptyADTException {
    if(isEmpty())
        throw new EmptyADTException("Nothing in the stack!");
    return (E) data[top];
}


For reference, this is how you'd make a generic array correctly:

public Stack(Class&lt;E&gt; klass, int capacity) {
    data = Array.newInstance(klass, capacity);
    ...


and then you'd need to pass a Class object into the Stack constructor:

Stack&lt;Integer&gt; stack = new Stack&lt;&gt;(Integer.class, 10);