I want to deploy Mongo image on a container service like amazon Fargate. can i write data to that container, if its possible to write data to the container where the data will be stored and they will charge it as a task?
Each Fargate task (PV 1.4) comes with 20GB of ephemeral storage included in the price. You can extend it up to 200GB (for an additional fee). See here. Again this space is ephemeral, if the task shuts down your disk is wiped.
One other option (in this case persistent) would be to mount an EFS volume to the Fargate task but probably not a great fit for a database workload.