Can I claim the payments i make as the cosigner on a student loan

No. 

For you to claim the student loan interest deduction, there are three requirements:

1. You must have actually paid it

2. You must be legally obligated to pay it (co-signing would qualify)

3. The student must have been your dependent at the time the loan money was used for education.  Note: he does not have to be your dependent now.

It depends. You cannot take a deduction for student loan payments, but you may be able to deduct the student loan interest paid since you are legally obligated to repay the loan as a cosigner. You can only claim the deduction if the qualified student loan is to pay higher education expenses for you, your spouse, or a person who was your dependent when you took out the loan. If the student was your dependent at the time that you took out the loan, you may be able to deduct the interest. (They do not have to be your dependent at the time that you made the student loan payments). If the student was not your dependent when you took out the loan, you will not be able to claim the Student Loan Interest Deduction. 

Please review the IRS topic Student Loan Interest Deduction and the TurboTax article What is a 1098-E: Student Loan Interest for additional details and eligibility information.

@stephaniejot