The system field ModifiedAt
(as the other system fields) is designed to be automatically managed and its value set to the respective date and time of the latest update. It is not possible to bypass this behavior.
One of the available approaches you may consider is using the X-Everlive-Override-System-Fields
header with a master key authentication and supply you own value for the system fields.
Another approach may be to make the sorting on another, custom field, for example, LastEditedAt
which will will allow to manage and set the value of this field as per your business requirements.
Let me know if this helps and if I may be of further assistance.