You will need to create a type that holds the contact object and the count:
B4X:
Type ContactAndTimes (Cont As Contact, Times As Int)
B4X:
Dim list1 As List
list1.Initialize
For Each c As Contact In listOfContacts
Dim t As ContactAndTimes
t.Initialize
t.Cont = c
t.Times = c.TimesContacted
list1.Add(t)
Next
'now you can sort the new list
list1.SortType("Times", True)