I was reading Closeable and AutoCloseable interface for the first time. As per my understanding we can't throw any exception apart from the IOException from close method of the Closeable interface and we can throw any possible exception like IllegalStateException only throw AutoCloseable Interface. But can we say that close() method of the Closeable method has exception in the signature.
Are you trying to ask if Closable.close() has exception in the method signature?
Yes it does, you can check the documentation here: Closeable.close(). It throws IOException.
void close() throws Exception
As per the documentation, Closeable extends AutoCloseable. We use it specifically dedicated to IO streams. Therefore it throws IOException instead of Exception.
From AutoCloseable.close():
While this interface method is declared to throw Exception, implementers are strongly encouraged to declare concrete implementations of the close method to throw more specific exceptions, or to throw no exception at all if the close operation cannot fail.