What happens when you connect batteries of different capacities i.e Ah in parallel or in series in a circuit?

Capacity in Ah is not directly related to voltage. If you have 3 AA batteries, each with different mAh ratings, you should be able to connect them in parallel or series to your hearts content. In series, the voltage will be additive: 3*(1.5volts) = 4.5 volts total voltage across all three batteries in series, assuming the battery voltage is 1.5 volts. In parallel, the voltage will be equivalent to 1 battery. In parallel, the three batteries are able to provide 3 times more current at 1.5 volts than if all three are in series at 4.5 volts.

Be careful when parallelling batteries of different voltages though. This is not a good idea, as they will try to force each other to match terminal voltage (voltage at the outputs of the batteries). An example: 1.5 volt AA battery, and a 12 volt car battery can be put in series - the total voltage will be 13.5 volts. The total current that can be sourced will be limitted by the AA's limit (much less than the car battery's limit). If put in parallel, the AA will try to force the voltage of the car battery down to 1.5 volts by drawing current into itself from the car battery. Alternately, the car battery will try to force the AA to 12 volts by pushing current into the AA battery. The AA battery will overheat, and likely catastrophically fail (blow up).