Final answer:
The auxiliary label that should be applied to a doxycycline prescription is 'Take with food'.
Step-by-step explanation:
The auxiliary label that should be applied to a doxycycline prescription during the filling process is Take with food. Doxycycline can irritate the stomach lining and cause nausea, but taking it with food can help reduce these side effects. It is important to follow the instructions provided by the healthcare professional or pharmacist.