Your town will only produce resources up to the capacity of your town. If you capacity for food is say 2 million when you reach that the farms stop producing food.
Your observation is accurate: in Vikings: War of Clans, resource production ceases once a town's storage capacity is reached. This is particularly crucial for food, as it is consumed by troops and is essential for various in-game activities.
To monitor and manage your resource capacities effectively:
"You have" – the current amount of the resource.
"Capacity: <name of the building>" – the maximum storage capacity of the resource.
"Capacity: Vault" – the total storage capacity, including the vault.
If "You have" exceeds the building's capacity, production will cease until the amount falls below the capacity threshold.