Does a ball resting on the Earth's ground have acceleration caused by gravity?
OK I don't understand anything.when I placed my mobile phone on the ground, its accelerometer shows nine point something m/s^2. So is that the value of its acceleration?
That is the value of the phone's proper acceleration. From the Wikipedia article "Proper acceleration":
proper acceleration is the physical acceleration (i.e., measurable acceleration as by an accelerometer) experienced by an object.
In the (non-inertial) coordinate system of the ground, the phone has no coordinate acceleration.
The proper acceleration of the phone is not due to gravity but, rather, the fact that the ground is preventing the phone from falling freely towards the center of the Earth. That is to say, the phone has an accelerated world line.
In summary, the phone has a proper acceleration of $g$ and a coordinate acceleration, in the coordinate system of the ground, of zero.