On demand breastfeeding?

Barb • mother of 2 amazing boys...after 2 1/2 years and 3 miscarriages, baby boy #3 is joining us May 2020!!💙👶🤰

Do you breastfeed on demand or by schedule? My baby is almost 4 weeks and so far my dr and health nurse tell me to feed every 2-3 hrs and no more than 4-5 hrs between feedings at night. But sometimes when I wake him he doesnt eat, falls asleep, or is fussy. What is best for keeping up milk supply?