The mayor of the town of Ekondo Titi, Kenneth Nanji, confirmed a deadly attack was carried out on a school there, but was not immediately able to provide the death toll.
The Cameroon-based Centre for Human Rights and Democracy in Africa said pupils aged 12, 16 and 17 and a French-language teacher were killed, and several others were wounded.
"Another senseless, outrageous ... murder of innocent children," the EU Ambassador to Cameroon, Philippe Van Damme, said on Twitter.
The region, one of two where English-speaking separatists have been fighting to form a breakaway state since 2017, was rocked by a similar attack last year when gunmen opened fire in a school, killing seven children.
Wednesday's attack comes just two months after hundreds of schools in the Anglophone South West and North West reopened years after they were forced shut by separatists.
There was no immediate claim of responsibility.
The crisis stems from perceived marginalisation of the Anglophone community by the French-speaking majority. Both sides have committed atrocities during the conflict, which has killed more than 3,000 people and displaced nearly a million.