Square issued a receipt to the applicants but the payments are missing to our account

What happens if an application accepts a payment and issues a confirmation and the money is not actually received?

Working as a non-profit summer camp organization we used jotform to collect payments for our summer camp. We now realized that forms issued receipts for payments via square, however none of the payments we received in our account. How is this resolved?

You can see the Transaction IDs are generated. This means that payments are made and received. You may consider asking Square support regarding these transactions, present them the IDs.

Your integration is correct. Maybe, you are viewing a different Square business account? You have selected "dsantana@gmys.org" as the Business Location in the integration. Please check if this is the account that you are currently viewing on Square. 

After calling Square they said it was an issue with the API...how do I contact jotform directly to inquire about an investigation. My non-profit not has send and received payment confirmations for thousands of dollars with no actual funds being deposited into our accounts. HELP!!!

As far as I can tell, your form is accepting submissions.  Have you connected to the correct Square account?  The transaction ID's are listed in with your submission data:

https://www.jotform.com/help/269-How-to-view-Submissions

You should be able to contact Square with those ID's to see where the payments are being sent.