I am paying my student loan that is under my dad's name (the borrower). Can I claim this deduction, since I have been paying off the loan?

Student loan payments are not deductible on a tax return.  Only the student loan interest paid can be entered on a tax return as an adjustment to income.

If you are not legally obligated to pay the loan then you cannot enter any student loan interest paid.

If you are legally obligated -

To enter student loan interest paid -

• Click on Federal Taxes (Personal using Home and Business)
• Click on Deductions and Credits
• Click on I'll choose what I work on (if shown)
• Scroll down to Education
• On Student Loan Interest Paid (Form 1098-E), click the start or update button

Or enter student loan interest in the Search box located in the upper right of the program screen. Click on Jump to student loan interest