Your baby needs to sleep in his/her own bed. If the air is cool in his room, bed him down with comfortable pj,s and little socks to keep him warm without the blankets. Let him toss and turn and be his own little sleeper. Don't use a pillow in his bed, and make sure it is a crib to keep him safe from falling onto the floor.
If he is waking up frequently during the night, I would suspect he is hungry. You may need to provide him with a little infant cereal and milk before bedtime to hold him over all night.
He/she may also feel too hot under the blankets and instinctively kick them off to feel cooler. Consider that a possibility. Maybe in summer, he would feel more relaxed with a relaxing bath before bed, and lightweight pj's. with no socks.
But for sure, your baby needs his/her own bed to sleep in. Even his own room if that can be arranged. He would likely sleep much better if you give these a try.
Let him sleep inhis own bed and kick as much as he wants to, some children are restl;ess, its okay, if he sleeps with you and it is disturbing you pop him in to his own bed.