Middle of night throws off day schedule

My three month old is on an eat play sleep schedule. He eats every 3 hours - 7, 10, 1, 4 and 7...

My question is what do I do if/when he wakes in the middle of the night?

Sometimes he will wake around 12:30 and 4 and sometimes he sleeps through until 5 and then our schedule gets all screwed up..

Should I try and get him back down with out feeding him? I feel like he would just be inconsolable if I didn’t feed him..

What do you moms do if you deal with this?

I’m not complaining I’m just trying to get him down at the same time at night along with my other son who is 2.