I assume you are using Square payroll. I do not currently use Square payroll but use a similar payroll service, and they handle filing the W3 to the feds with the W2's they've produced for our employees. I don't know that this is what happens with Square Payroll but, hopefully someone that knows more can point you in the right direction.
@Kpay is there someone on this board from Square Payroll?
I work on the Square Payroll product team - happy to help out with your question.
Square Payroll will generate W-2s, file them, and send them to each of your employees. We are planning on generating Form W-3 as well, but since that form is not required because we file Form W-2 electronically, these will likely be done later in the month.
Your W-2s are currently available for preview in the Tax Forms section of your Square Payroll dashboard.
Let me know if you have any other questions!