I would consult his parents and ask them if he exhibits these behaviors at home. I would ask them what strategy they use to adjust his behavior, or if they don't have an issue at home, what would they suggest. Depending on the age of the student he may be showing signs of a physical or emotional disorder. Getting the parents involved to find a solution would be the first step.

It is sometimes helpful to know exactly why he is exhibiting these behaviors. Does he do it at certain times? When he is hungry? Bored? Thinking? This may help you avoid situations where he is moving like this. If he exhibits these behaviors constantly and they are that disruptive to class, that seems to be slightly more than just being fidgety. In that case I would suggest potentially referring him for testing.

Try implementing a reward system for when the student DOES sit at his desk correctly or walk in line appropriately. Class Dojo is an excellent site to look at that will allow you to create your own categories of rules and expectations (such as walking in line correctly and sitting at desk quietly). At the same time, if you do Class Dojo with your entire class and just have these types of rules mixed in for him (and general ones for other students), that particular student will have something to work towards without feeling singled out. In my opinion, a student is always more willing to do something when there is a reward involved--focus on the positives instead of the negatives.

I have him walk next to you in the line and form a reward system for him in the hall. This way you can closely monitor his behavior and positively reinforce the behaviors you are expecting him to show. Depending on the reward system, he can earn something once he has reached a certain number of points. A sample reward could be the use of a rolling chair in the classroom. This is often something students desire to have in the classroom and would also serve as a way for the student to get any extra energy out without disrupting the class. You may also ask him to serve as a role model for the other students in the hallway. This may give him responsibility and encourage him to show the appropriate behavior.

He needs to learn there is a time and place for his movements. So be sure to allow him that time and place to move around and do those things but through the halls is not one of them. Maybe creating a positive reinforcement reward system for him might be helpful.

I make my students who refuse to fall in line walk on the opposite side of the hall. Usually the negative peer pressure makes them stop. Also- I have found that letting students complete reading or assignment while sitting on the floor minimizes (surprisingly) the need for such students to be so disruptive.

I would have a class rule about sitting still during class, staying focused and not distracting other students. Also I would have a particular way the students are supposed to walk in the hallways. I have seen students had to walk with "tail feather." They had to have their hands behind their back forming a tail feather like a bird. Also, most times a reprimand will not solve the problem long term so it is a good idea to have a reward/consequence system.