Payroll Tax Liability Quarter issue

Hello, I'm having problems finding the answer to this question anywhere online. 

The company I work for has over 40 employees, our pay periods are 1st-15th and 16th-30th/31st.

The issue I'm having is figuring out is when I'm depositing payroll tax liabilities what quarter they go into when moving into another quarter.

So for instance this recent pay period of 3/16 - 3/31, paychecks went out today 4/5/24. What quarter do these go into for state and federal payroll taxes.

From what I understand since the payroll period was during March that these payroll taxes from the 4/5/24 check would be applicable to Quarter 1 2024 and not Quarter 2 2024.

Is it always based on payroll period or is it based on the actual check date? 

Any information on this would be great, as when on Quickbooks the period says 4/3/24-4/6/24 but I'm not quite sure thats right.

Thank you.