Hi,
A battery is a storage of energy.
The Ah value is proportional to the energy it can store (indeed Ah × V = VAh = Wh = energy)
So it's like a fuel tank in a car. If your car needs 8 l/100km and you want to go 500km then the tank needs to be 40l (or bigger). If it is 50l, then there is no problem. The car still will draw just 8l/100km.
But: if you have 4 batteries each 1.2V / 1000mAh and ...
you connect them in series, then you get 4.8V, 1000mA
(If you connect them in parallel you get 1.2V 4000mAh)
Klaus