You can try

{
     "CreatedById" : "<Record ID of user>"
}
//or you can use
{
     "CreatedBy": { "<Unique Field in User>" : "<value>"}
}

I created the example to update that field following link

You might want to first check that the user you used in the CreatedById field, besides API account, also have permission to create record.

If that's already the case, you might want to try using this method instead:

{
     "CreatedById" : "<Record ID of user>"
}
//or you can use
{
     "CreatedBy": { "<Any Unique Field in User>" : "<value>"}
}

Please see "How to assign value to CreatedById fields via REST API in Salesforce" for detailed steps.

I am not sure the value of the desired User has the permission to create the record or not. But if you want to assign value to CreatedById

{
     "CreatedById" : "<Record ID of user>"
}
//or you can use
{
     "CreatedBy": { "<Unique Field in User>" : "<value>"}
}

I created the example to update that field following link

You can try

{
     "CreatedById" : "<Record ID of user>"
}
//or you can use
{
     "CreatedBy": { "<Unique Field in User>" : "<value>"}
}

I created the example to update that field following link