Your exhaustion and your repeated cry to Jesus are heard, and it is understandable that you feel worn down by night after night of waiting until nearly morning for your son to sleep. This is hard on you and it is not good for him, and the Lord sees both of you in it.
Scripture presents God as the God of patience and comfort. He is patient in working out His purposes, waiting as a farmer waits for the precious fruit of the harvest. We are told that we have need of patience, that after we have done the will of God we might receive the promise, and that through faith and patience we inherit what He has promised. If we hope for what we do not yet see, we are called to wait for it with patience. That patience is not passive resignation, but a hopeful trust that God is at work even while we are still asking and waiting. He hears every prayer you have prayed for your son, and He invites you to keep bringing this need to Him.
God also gives wisdom for training children. The Scriptures say to train up a child in the way he should go, and that phrase points to a thoughtful, consistent, systematic training that recognizes each child is different in personality and needs. There is a natural foolishness bound up in the heart of a child, and loving, steady instruction and boundaries are part of driving that foolishness away. To leave a child entirely to himself or to be lax because you do not want to cause conflict will not help him, and it will bring more exhaustion to you. Loving discipline is not harshness, it is the patient work of a parent who teaches a child how to walk, expecting stumbles and falls along the way, and gently guiding him again and again.
Jesus showed how precious children are when He took a little child into His midst and said that whoever receives one such child in His name receives Him, and He warned not to despise these little ones. Your son is deeply valued by the Lord, and your work in caring for him, even in these sleepless nights, is significant ministry.
In practical terms, this is a call to combine continued prayer with patient, consistent training. Ask the Lord for wisdom to establish a clear and loving bedtime pattern and to hold it with kindness and firmness each night, understanding your son's unique needs and temperament. It will likely take time and repeated guidance, just as teaching a child to walk takes many attempts, and God will give you patience as you persevere.
May the Lord, who is your comfort, strengthen you in this weary season, give you rest, and work in your son to establish healthy sleep. Keep asking, keep trusting, and keep training with love, knowing that God is patient with you as you learn to be patient with your child, and that He is able to bring the fruit in its proper season.