3 Month Notice Period !!

Bro, ask the new company to give you joining bonus and negotiate in your existing company for the same amount to get relieved in 2 months. This would offset the loss of pay and both sides get benefitted. Most of the time since you would still be 2 months in your existing company, managers are more inclined to give it a shot and find your replacement.
PS- see if you can make the same work for 6 weeks as well. It will depend on how critical you are to your existing organisation.

Ask politely to your manager if he doesn't agree. We have no choice. Goof up on KT and make sure to look very happy during the notice period . Smile more especially when the manager is seeing you. Talk to everybody in the office and be extra friendly. Every time your boss sees you smile he should have acidity. It's a pin prick, but it will be straight to his heart. A happy resigned team member is the second worst feeling a boss can have. This is what I did. All je could do was relive me on Friday and deduct 3 days pay for not serving the notice period till Monday.

Even I had to serve my 3 months of notice when i resigned from Amdocs, I tried to negotiate the notice period with my manager, but he refused it.

Tell you new company that notice period is strictly 2 months.
Then, use your earned leaves, some negotiation and some buy out to reduce your 3 month notice period to 2 months.
Make sure, negotiate on working days not total days.
There are 22 working days in a month. This can be reduced to 0 with all 3 negotiations.

@FakeMonkey36 Just talk to your manager, first humbly and then assertively. As per law, they can’t force you to complete the notice period but only recover salary for non-served days. I’m parallel also talk to the destination org to buy this out. Almost all orgs will happily buy out notice period.