A bursary is a grant, especially one awarded to someone to enable them to study at university, college or higher education.
Mr Mahama, speaking at Somanya in the Eastern Region on Saturday, said the implementation of the free SHS is absolving all the fiscal space of the government.
Due to that, he said the government was unable to pay money owed the District Assembly Common Fund, NHIS, Getfund and salaries of public workers.
He said: "And the point is we must adopt a system were those who can afford to pay are able to pay. I can afford to pay my son's fees, why should you give me free senior high school?
"Identify those who need it, who cannot afford to pay and give them bursaries so that they can pay those fees and those who can afford to pay, let them go ahead and pay.
"The problem this government is facing, and it is in their own interest, is that free senior high school is absolving all the fiscal space they have. And so every money you have, you are having to put it into free senior high school. So you can't pay district assemblies common fund, you can't pay NHIS, you can't pay Getfund, you can't pay other salaries and things because all your money is going into free senior high school. And the problem is that, this is only first year. "
President Nana Akufo-Addo has said the introduction of the free Senior High School has given opportunity to over 90,000 children to be enrolled in 2016.
According to him, the 90,000 would have missed on the opportunity to have secondary education if it had not been for Free SHS.