I'm not sure what you are asking but a better version would be 'I checked the mail box four times this day: twice in the morning, once at noon and once in the afternoon.'
'Respectively' is only used when you need to clarify the order in which something happens, and mornings, noon, and afternoons can only happen in a certain order, so it is redundant here.
i.e.
John and Jim enjoyed cakes and tea means they both had cakes AND tea.
John and Jim enjoyed cakes and tea respectively means John enjoyed the cakes and Jim enjoyed the tea.