What's the criteria to become a government teacher in primary schools? Will it apply for B.Ed correspondence students?

It is mandatory to do primary teacher training in BTC and you have to qualify the state level TET or CTET. In most of the states B.Ed is not an essential degree for teachers in primary schools.

For government teachers, you should have cleared B.Ed and qualified the state government TET exam or CTET. Then if vacancies are there, you can apply. All the best.