I need my motor to be powered with 12V, 5A for 1 hour continuously. How can i decide the Ah rate of the battery. Please suggest some lithium ion battery for the specification
The Ah rating is a measure of charge - how many amps the battery can supply, for how long.
In your case you need 5A for 1 hour, and that is simply 5 Ah. You multiply the current by the time required, to get the charge needed.
Next, The voltage rating is basically how many cells are used to make up that battery. You can't control that - you just have to get a battery that has the correct number of cells.
So the full specification you need is: something rated for approximately 5Ah at approximately 12V. (I can't advise on which one you should buy, as there are so many other factors that have to be taken into account.)