At approximately three months of age your baby will likely sleep about 15 hours out of each 24-hour period, and two thirds of that sleep will take place during the night. Most babies will have settled into a daily sleep routine of two or three sleep periods during the day, followed by "sleeping through the night" for 6 to 7 hours after a late-night feeding.
You can help adjust your baby's body clock toward sleeping at night by avoiding stimulation during nighttime feedings and diaper changes. The act of breastfeeding itself provides frequent eye and voice contact, so try to keep the lights low and resist the urge to play or talk with your baby. This will reinforce the message that nighttime is for sleeping.
Keeping the door closed to keep out well-meaning but vocal older children, spouses and pet will also keep reduce stimulating your infant. Avoid the use of musical mobiles or toys as a way to lull your infant back to sleep after night-time feedings. This will also help to reinforce that nighttime is for sleeping. And, as with adults, overly tired infants often have more trouble sleeping than those who've had an appropriate amount of sleep during the day.
So, keeping your baby up thinking that he or she will sleep better at night may not work. You may find that when your infant sleeps at regular intervals during the day, it will be easier to put them back down to sleep after night-time feedings.