Method One: Mapping the value
To import in the transaction map the following fields. So for example if you want to import a custom field of Yellow into the Color custom field you would set the CustomFieldName1 = Color and the CustomFieldValue1 = Yellow
||Name of the Custom field 1 ie Color
||Value for the Custom field 1 ie Yellow
||Name of the Custom field 2
||Value for the Custom field 2
||Name of the Custom field 3
||Value for the Custom field 3
If you need more than 3 custom fields at the row level then you also have the Other1 and Other2 fields available, you will need to make those visible on the QuickBooks Template in order to see those in QuickBooks.
Note: This is for Custom Fields at the Item line level, for custom fields to appear at the header level (ie Customer) you should look at using automatic propogation or the Other and FOB fields
Method Two: Automatic propagation
This is achieved by making sure that the custom field values are already assigned to the respective list item (ie item, customer, vendor) prior to importing the transaction, see more on importing custom field lists, then when the transaction is imported the Custom field value will appear by default alongside the item, customer or vendor. This is called automatic propagation.
If you want to see this in action create an invoice in QuickBooks then add an item that you know has custom fields values assigned to it and you will see the custom fields and respective values automatically appear (make sure you are displaying the custom fields on the template). The same automatic propagation happens when Axis imports transactions.
Error - The specified custom field cannot be used by the list or transaction element - The error is due to the custom field that you are importing is not associated with the Name or Item you are importing it against. So for example you have a custom field for a customer but the custom field is only associated with an item. You an resolve this by setting up the custom field to be associated to the Name as well as the Item.