There are several methods to help a baby with a cold expel phlegm, which are as follows: First, you can give the infant some Western or traditional Chinese medicines that help expel phlegm to aid the removal of mucus. Second, gently patting the baby's back can also facilitate the expulsion of phlegm. Third, if possible, using a phlegm suction device can help the baby expel phlegm. Fourth, administering nebulized medications that help expel and remove phlegm can be effective. Lastly, it's important to treat the cause of the baby's cold-related phlegm production. Most colds are caused by respiratory viral infections, so taking antiviral medications can be very effective. If the cold and phlegm persist, be aware of the possibility of a secondary bacterial infection, which, if present, may require antibiotic treatment. (Note: Medication should be used under the guidance of a doctor.)