Cna I sue this female that I found out that my husband was having an affair with, is it a such thing I can do I live in NJ

Sue her for what?
Anyone can file civil suit against anyone, but you will lose for an affair. The person you should consider suing is your husband - it's called a divorce.

Such lawsuits were frequent in the past; maybe 100 or more years ago. It was called "alienation of affection". I doubt if it's done any more.

Such lawsuits were frequent in the past; maybe 100 or more years ago. it was called "alienation of affection". I doubt if it's done any more.

Nope! Look at South Dakota legislation and Court practice!
Same in Mississippi /Fitch v. Valentine, 959 So. 2d 1012 (2007),North Carolina and some other states.;):p:p:p:p:p
Even in Alaska/ I guess you know the law/no legislation was enacted to abolish the right to bring an alienation of affection lawsuit.