rent paid calculation under?

Deduction u/s 80GG

upto how much we can claim in one financial year as mine is 1,20,000 per year.

Deduction –the lowest of these will be considered as the deduction under this section- (a) Rs 5,000 per month (b) 25% of the total Income (income to exclude long-term capital gain, short-term capital gain under section 111A and Income under section 115A or 115D and deductions 80C to 80U. Also, income is before making a deduction under section 80GG). (c) Actual Rent less 10% of Income (income to exclude long-term capital gain, short-term capital gain under section 111A and Income under section 115A or 115D and deductions 80C to 80U. Also, income is before making a deduction under section 80GG).

so total 60000i can claim only?

Yes. But you can claim either deduction u/s 80GG or HRA if you are an employee receiving HRA from your employer.