Well, I guess the correct english name for these badges will be
Badge, marking the graduation from the schools of infantry ensigns, which were filled up with the students of the higher educational establishments.
Theoretically all shields on eagle's breast should be covered with green enamel and bearing gold letters (initials of schools). But on practice we observe different colors of enamel or no enamel at all. Same goes for the initials of schools...
Initials usually very simple.
Russian letter Ш (for школа/school).
Sometimes additional letter П (for прапорщик/praporchik/ensign)
First letter in the name of the town where school located + arab numerical (in case there are several schools in one town)
As for today the following initials are decoded