Baby sleeps bad after 3 am

Na

So after 3 am every single night my son wakes up every 40-60 minutes. He’s sleepy, not hungry, I feed him at three but no matter what he just doesn’t do longer stretches.

He goes to bed at 8 pm, sleeps well till 11.30-12, eats and then wakes up at 3, I feed him, put him to bed and the hell starts after 40 minutes.

What can I do to improve his sleep after three ?

He’s not a good mapper either. I have to hold him for naps and prolong his naps since he is up after 30 min..

He’s turning 3 months old this week.