I got a new opportunity in a startup with a good hike as compared to current organization, my notice period is 30 days and still my manager wants me to stay in the company for atleast 3 months, I am so in a dilemma. What should I do?

startups are soul squashing rip offs
which will leave you burnt out and jobless in 6 months.

How ever thats for your future employer to decide if they‘re ok with having to wait 3 months.

Your boss is haggling. Shitty and unprofessional thing to do. If you're on good terms, offer 6 weeks, but only if your new employer will wait.

If your current boss is a tool, give what's obligated and nothing more.

What @SortOfTested said, three months is 3 times as long and you're not obligated to give them Jack shit beyond those 30 days. Companies doesn't care about you so loyalty seldom pay off

Make sure you do things properly. Write an official resignation letter, if you haven’t already, stipulate the day of your leaving and be extra nice. Leave it at that, then there will be no doubt or ambiguity. Don’t feel bad. Here’s a good example stolen from Monster