I used to wake up at 4 am having anxiety every morning for years. I think it’s partly biological and may have to do with blood sugar levels and the like. So the first thing to keep in mind is that this may well be caused by a physical factor and is not all psychological or spiritual in nature. Think about ways you might help prevent late night anxiety - for instance, no caffeine after a certain hour, consume a protein snack late in the evening (like milk or a protein bar), adjust your sleep schedule.
To the extent it is psychological or spiritual, I would recommend more prayer, and not just at 3 am. The Divine Mercy prayer is good. “Jesus, I trust in you.” If you are oriented towards Scripture, you can try reading some, especially the Gospels. If you are comfortable with Mother Mary, you can pray rosaries also, or “We fly to your patronage, o Holy Mother of God…” short prayer. If there are particular saints you find reassuring, such as Padre Pio who said “Pray, hope and Don’t Worry”, then ask for their intercession.
When you pray, you get grace. Grace helps remove anxiety and doubt.
Going to weekday Mass and Adoration when your schedule permits are also good ways to get grace.
Put some sacramental objects like a crucifix or your favorite rosary or Bible close to your bed so when you wake up, you see it right away and can grab it if you need to hold God’s hand. I always have a Rosary or two within easy reach (my parents did the same).
I stepped up my prayer this year. I still wake up in the night (I’m up right now) because I’m a night owl naturally and also work across many time zones. But the amount of anxiety I suffer has greatly diminished.
God bless.