What should I do when I'm ready to pay in lieu of notice and the company is not agreeing?

I've put my resignation where in my notice period is of 3 months and I want to pay the same in lieu of notice but my employer is not agreeing on the same and in my offer letter it is written "Consequent to confirmation, the company may terminate your services by serving 3 (three) months' prior notice or on payment of an amount equivalent to 3 (three) months' gross salary/remuneration in lieu of the notice period, without assigning any reason thereof.
In case you decide to leave services of the Company consequent to confirmation, you will be required to serve 3 (three) months' prior notice to the Company or will pay an amount equivalent to 3 (three) months' gross salary/remuneration in lieu of the notice period, without assigning any reason thereof."

What should I do when I'm ready to pay in lieu of notice and the company is not agreeing?

When the employer rejects the buy out offer of a resigning employee and insist on serving the notice period, it's a tricky situation for the exiting employee.
If he simply walks out on his own by remitting the amount of notice salary, the employer would treat this as unauthorized absence and initiate disciplinary action which could result in the employee's dismissal from service. Till such time the exited employee would be deemed to be in the service of the establishment.
The prospective employer may not allow the employee to join without a formal relieving orders from the previous employer for it could result in dual employment for statutory purposes.

Even if the prospective employer does not mind the relieving orders from the previous employer, still the problem of dual employment would be there if the previous employer treat the case as of abscondence. Again, it may be an insurmountable impediment in his future employment if the employee whenever switches jobs.

If the employee's resignation is for any reason other than reemployment elsewhere once for all, may be he need not bother about a formal relieving order as he had complied with his part of the exit clause of the contract of employment against which the estranged employer has no legal remedy.

Therefore, the poster should consider all these things and come to a rational conclusion. It's better for him to convince his present employer about his dire necessity of immediate change of job and make his exit formal and peaceful.