Hi all,
I found a new job, and quit my current job, gave company 2 weeks notice, but they said I need 3 weeks notice.

in my employment contract, there is:

"two weeks notice must be provided in the first year, and one additional week for each subsequent year worked."

I don't understand what this mean, could anyone please help to explain this.

I worked 1 year and 3 month, do I really need 3 weeks notice?

If I dont give them 3 weeks notice then can they may give a poor reference in the future; at that point I would sure for defamation.

As per your agreement, you are obliged or required have to give 2 weeks notice only. This is so, considering that you have only 1yr and 3mo stay at the company. However, complications may arise, if the 3 mo will be interpreted to mean or considered as 1 year for purposes of that specific provision. That would still be debatable. For now, the 2 week notice you have given, I believe was sufficient. Thus, you have done your part already. It is hard to speculate what would the company say as to your performance or reference...you can sue for defamation only be if specific facts exists...