As a new section NCO, what would be the best way to deal with squad leaders who skipped the chain of command (myself)?

The question seems a bit confusing -- and your comment makes it even more so.
I've never seen a "section" that had "squads" -- which makes it hard to envision a "Section NCO" (whatever that is) having Squad Leaders going over his head to the Platoon Sergeant.

Even when I ignore that and just assume that your unit has squad leaders under a Section NCO. I'm not sure what the problem is. In the situation you describe, the PSG or PL's first question to any squad leader who comes with an issue would have to be "Have you spoken to your Section NCO about this?" Just as the PL would ask if the soldier had spoken with the PSG.

"Skipping the chain of command" is not always inherently wrong. Every military leader is expected to deal with issues experienced by any of their subordinates -- regardless of whether they call it a formal "Open Door" policy or simply good leadership. But at the same time, the first question should always be whether the problem has been discussed at a lower level and what the results were.

With that in mind, and assuming that your PSG and PL are competent, I note that your describe yourself as a "new section NCO" -- I would think (and hope) that your PSG isn't upset that squad leaders are coming to him directly so much as that he is trying to help you develop your leadership skills by handling whatever issues might arise within your section.

What you do about the 'problem' depends greatly on what you think the cause of the problem is. Are your Squad Leaders going directly to the PSG because that's what they have always done? This would be the case if your position was recently created or if the position had been vacant for a while before you. Are they going to the PSG directly because they don't have confidence in your ability to handle their problems? This might be because the last section NCO didn't do well, or because they don't think you know what to do, or perhaps because you were promoted from within the section and they still see you as "just one of the guys". Are they going to the PSG because they see you as the problem or part of the problem?

There are ton of possible reasons for the situation and even more possible nuances of the relationships within the section and platoon.

In general I don't think it is a matter of needing to "deal with" the squad leaders unless you are convinced that bypassing you is a deliberate attempt to undermine your authority. It seems that the first step is to ensure that the squad leaders know the chain of command and realize you are there to help resolve whatever issues they might have. This might involve speaking with them together or individually, depending on your personal style and your impression of the situation. Another possible approach is to start by talking with the entire section to remind everyone that you are available to handle any issues but that whenever possible they should utilize the chain of command by starting with their squad leader. This reinforces the role of the squad leaders in the chain of command as well as reminding those squad leaders that you are the next link in that chain.

Speak to each one privately. Remind them of their duty to obey orders. Remind them that your evaluation may determine their future promotion. Ask yourself why they go over your head. Review your leadership qualities. Get feedback from an equal or higher ranked soldier in your unit.

Remember everything is about success. Training should fit the point of concern. platoon sergeant need to meet with leadership for an evaluation, What do they see in you the needs to be improved.

So for the record you are the NCOIC as a CPL, you have subordinate squad leaders who are not NCOs. That is strange to begin with.

If this is the case then it is important to know whether they did this once or multiple times. Also important is how long you have been there squad leader.

This can range from a first time conversation trying to discern why the did that and what it was about.

I could go on, if you provide more details you can receive better guidance from the group.

NCO support channel vs. Chain of Command. First you need to understand your roles and responsibilities. Your PSG/Section Sergeant should outline what is expected of you. As far as what you can do to Squad leaders that jumped you, again, you’re a new Corporal so I would avoid being too heavy handed. But you can verbally counsel them and let them know what is expected of them and if the at doesn’t work, counsel on paper. That’s about as far as your course of action goes. If the platoon leadership sees this as an issue , they should address it early to prevent a continued pattern.

This is a test. You are the new Junior leader and your Boss wants to know how you will hold your ground.

Don't go over the top. Sit down with each Solider and do an initial counseling to establish a baseline with each of them. Go over expectations, goals and etc. Learn what they have done, what they can do and what they wish to do in the future. Also use this time to go over your expectations. Ensure they understand the chain of command and live it there. Once you have a baseline to work with you can move forward without any shadows of doubt knowing everything has been covered

You are a Private. You are not part of the Chain of Command. Last time I checked, Chain of Command at the Company Level is from Squad Leader to Platoon Leader to Company Commander. Support Channel would be Team Leader to Section Leader to Squad Leader to Platoon Sergeant to 1SG.

If you notice, the only NCO in both Chains is the Squad Leader. You, as a Section NCO reports to the Squad Leader. They don't report to you.

I’m serving as a platoon sergeant for 25 Soldiers. My peer is the NCOIC and runs operations. Can you imagine running a shop of 25 people if they jump the line? I’m not saying I won’t help them if they come to me. But think about the stress on my end. Eventually I would like to go home at the end of the day. Once or twice is not a big deal, but a trend will make me upset. I will call the CPL and SGT in and ask why I’m doing their jobs. If it continues the CPL will get a negative counseling and the SGT will have it reflected on their NCOER as incapable of taking care of Soldiers.

As a "New" leader you are going to have to assert yourself, confront the individual find out what is their problem and why is it that they feel you can't seem to fix their problem. You command is aware of the situation and are relying on you to fix it. You are an NCO now, fix it.

Look inwards. It is 100 percent the right of any Soldier to address an issue with a higher member of the command. Hence.. why the open door policy exists. Look at your leadership style and try to dig into why during that instance your Soldier felt like they couldn't address the issue with you. Sometimes they just want to make waves. However, at other times you are not presenting yourself as a "trusted agent".. or your style/approach to that individual might be the problem. Respect for your position should be demanded.. trust on the other hand isn't something as easily given as is lost. Always look down before you look up. Check yourself first. People first is not about coddling. You can be a hard charging leader and a shoulder when the situation demands it. Learn to shift gears and know your Soldiers. Many new NCOs make the mistake of thinking every slight needs a response. Knowing the difference between an intentionally subversive act and someone simply not trusting you to listen and take action is something that will come with time. Hope that helps.