Back in 2011 when I was 4months pregnant I send a email to my son father girlfriend: I started by saying that we don't know each other but I'm carrying his baby and she should know. The emails was back and forth and I threatned her. Now in November of 2012 she decided to file for an order protection in the complaint she stated that we had intimate relationship and we share a kid in common. She basically lied under oath. I pleated no contest but can I sue her for lying about our relationship. Also when she was granted a temporary order protection the same day she made a false police report stating that I called her from s public phone and had me arrested. Investigation was made an
Id they foundout that she lied. What can I do about the false accusations andherlieing about our relatipnship

How were you harmed by this? Sure you can sue, but I doubt if you would win.

I'm sorry but I don't understand - you threatened her, but then had an intimate relationship with her, or she's just making all that up, or I'm reading this all wrong? And what does it mean to 'share a kid in common?'

No her and I never had a intimate relationship she stated that and that we share a kid in common on the petition. I pleated no contest because what happened in 2011 but the fact that when presented to the judge she lied under oath when the judge asked how we related? she said she was my ex(BS) so been that its family court and she said: she fear for her kids she was granted a OP... than the same day she file a complaint in the pct and stated that I called her from a public phone... the case was under investigation turned out she lied..
1.Can she be granted a OP even though the email was sent after more than a year? 2.even if I pleated no contest can I sue her for false accusations and lying about been my girlfriend?

You plead no contest, which means that you accepted what she was claiming, as fact. It's too late to go back and change your plea.

Anyone can sue, but what would you sue for? What money are you out because of her accusations? You sue someone because you've lost something due to their behavior or actions. So, other than being upset about what she said, what have you lost? They can't give you back yourself respect in court, and you're not out any money, so how can the courts make you whole?

What about her false police reports,lying that I called her and had me arrested after she was granted the temporary OP

What about them? How were you monetarily damaged by them?

We're not saying you were wronged by this woman, but to sue her requires more than just being wronged.

Criminal court is for crime.
Family court is for family disputes.
Civil court is for monetary damages, so a dollar amount has to be sued for, and either awarded (sometimes in a different amount) or denied by a judge. The burden is on the plaintiff (you) to prove that you lost that amount of money. You can try for pain and suffering, but those are often tossed out of court.
You can try in Small Claims (a kind of civil court) for about a $50 filing fee, but don't count on winning, or even getting paid if you do win. Small claims judges decide quickly, and you have to be very well prepared and able to articulate your claim. Lying isn't something you can sue for unless there is a monetary reason attached. Lying under oath should have been addressed when you were in court, instead of pleading no contest. So there's really no hope for any of this.